034IN "Fundamentals of Automatic Control" - Introduction to MATLAB
Part 2 - Numbers, Arithmetic Operations, Formats and Variables
This is the second MATLAB live script of the collection 034IN "Fundamentals of Automatic Control" - Introduction to MATLAB, devoted to introduce the MATLAB environment and tools for solving practical problems related to the topics of the 034IN course, i.e. performance analysis of dynamic systems, design of control law for continuous-time linear dynamical systems, approximate discretization of a continuous-time control law etc.
Use this link to go back to the main live script of the collection.
Objectives
The aim of this module is to enable you to enter an arithmetic expression in MATLAB and understand the results produced, particularly when these results involve scientific notation, complex numbers and Inf (Infinity) and NaN (Not a Number).
What you should know by the end of this module:
- the importance of being very precise when entering arithmetic expressions, particularly when brackets are required;
- how to enter numbers using scientific notation and how to change the format of the answer displayed in the MATLAB Command Window;
- how to enter complex numbers and how to find real and imaginary parts;
- the meaning of Inf (infinity) and NaN (Not a Number);
- what is a valid variable name;
- how to use = to assign a value to a variable and how to clear a variable;
- MATLAB predefined variables (constants), pi, i, j, eps, etc. ;
- how to examine the value of a variable, how to list the variables in the current workspace, how to get extra information about the variables and finally how to remove them from the current workspace.
With a Little Help from the 'help' Command!
Here is a list of the main categories of topics available using the help command
General purpose commands
help general
General purpose commands.
MATLAB Version 25.2 (R2025b) 28-Jul-2025
General information.
syntax - Help on MATLAB command syntax.
demo - Run demonstrations.
ver - MATLAB, Simulink and toolbox version information.
version - MATLAB version information.
verLessThan - Compare version of toolbox to specified version string.
logo - Plot the L-shaped membrane logo with MATLAB lighting.
membrane - Generates the MATLAB logo.
bench - MATLAB Benchmark.
Managing the workspace.
who - List current variables.
whos - List current variables, long form.
clear - Clear variables and functions from memory.
onCleanup - Specify cleanup work to be done on function completion.
Pack - Consolidate workspace memory.
load - Load workspace variables from disk.
save - Save workspace variables to disk.
saveas - Save Figure or model to desired output format.
quit - Quit MATLAB session.
exit - Exit from MATLAB.
Managing commands and functions.
what - List MATLAB-specific files in directory.
type - Display MATLAB program file.
open - Open files by extension.
which - Locate functions and files.
pcode - Create pre-parsed pseudo-code file (P-file).
mex - Compile MEX-function.
inmem - List functions in memory.
namelengthmax - Maximum length of MATLAB function or variable name.
Managing the search path.
path - Get/set search path.
addpath - Add directory to search path.
rmpath - Remove directory from search path.
rehash - Refresh function and file system caches.
import - Import packages into the current scope.
finfo - Identify file type against standard file handlers on path.
genpath - Generate recursive toolbox path.
savepath - Save the current MATLAB path in the pathdef.m file.
Managing the java search path.
javaaddpath - Add directories to the dynamic java path.
javaclasspath - Get and set java path.
javarmpath - Remove directory from dynamic java path.
Controlling the command window.
echo - Display statements during function execution.
more - Control paged output in command window.
diary - Save text of MATLAB session.
format - Set output format.
beep - Produce beep sound.
desktop - Start and query the MATLAB Desktop.
preferences - Bring up MATLAB user settable preferences dialog.
Operating system commands.
cd - Change current working directory.
pwd - Show (print) current working directory.
perl - Execute Perl command and return the result.
Debugging.
debug - List debugging commands.
Loading and calling shared libraries.
calllib - Call a function in an external library.
libpointer - Creates a pointer object for use with external libraries.
libstruct - Creates a structure pointer for use with external libraries.
libisloaded - True if the specified shared library is loaded.
loadlibrary - Load a shared library into MATLAB.
libfunctions - Return information on functions in an external library.
libfunctionsview - View the functions in an external library.
unloadlibrary - Unload a shared library loaded with LOADLIBRARY.
java - Using Java from within MATLAB.
usejava - True if the specified Java feature is supported in MATLAB.
See also lang, DataTypes, iofun, graphics, ops, strfun, timefun,
matfun, demos, graphics, datafun, uitools, doc, punct.
Control System Toolbox -- General Utilities.
(R2025b) 28-Jul-2025
abcdchk - Check consistency of A,B,C,D matrices.
db2mag - Convert magnitude from absolute value to dB.
mag2db - Convert magnitude from dB to absolute value.
padecoef - Pade approximation of time delays.
residue - Partial-fraction expansion (residues).
resi2 - Residue of a repeated pole.
ss2tf - Convert state-space system to transfer function.
ss2zp - Convert state-space system to zero-pole.
tf2ss - Convert transfer function to state-space.
tf2zp - Convert transfer function to zero-pole.
tfchk - Check for proper transfer function.
zp2ss - Convert zero-pole system to state-space.
zp2tf - Convert zero-pole system to transfer function.
Folders named general
Operators and special characters
help ops
Operators and special characters.
Arithmetic operators.
plus - Plus +
uplus - Unary plus +
minus - Minus -
uminus - Unary minus -
mtimes - Matrix multiply *
times - Array multiply .*
power - Array power .^
mldivide - Backslash or left matrix divide \
mrdivide - Slash or right matrix divide /
ldivide - Left array divide .\
rdivide - Right array divide ./
idivide - Integer division with rounding option.
kron - Kronecker tensor product
pagemtimes - Page-wise matrix multiply
pagetranspose - Page-wise transpose
pagectranspose - Page-wise complex conjugate transpose
pagemldivide - Page-wise left matrix divide
pagemrdivide - Page-wise right matrix divide
tensorprod - Tensor products between two tensors
Relational operators.
eq - Equal ==
ne - Not equal ~=
lt - Less than <
gt - Greater than >
le - Less than or equal <=
ge - Greater than or equal >=
isapprox - Equal within a tolerance
Logical operators.
and - Element-wise logical AND &
or - Element-wise logical OR |
not - Logical NOT ~
punct - Ignore function argument or output ~
xor - Logical EXCLUSIVE OR
any - True if any element of vector is nonzero
all - True if all elements of vector are nonzero
Special characters.
colon - Colon :
paren - Parentheses and subscripting ( )
paren - Brackets [ ]
paren - Braces and subscripting { }
punct - Function handle creation @
punct - Decimal point .
punct - Structure field access .
punct - Parent directory ..
punct - Continuation ...
punct - Separator ,
punct - Semicolon ;
punct - Comment %
punct - Invoke operating system command !
punct - Assignment =
punct - Quote '
punct - Double quote "
transpose - Transpose .'
ctranspose - Complex conjugate transpose '
horzcat - Horizontal concatenation [,]
vertcat - Vertical concatenation [;]
subsasgn - Subscripted assignment ( ),{ },.
subsref - Subscripted reference ( ),{ },.
numArgumentsFromSubscript - Number of arguments for indexing methods
subsindex - Subscript index
metaclass - Metaclass for MATLAB class ?
Bitwise operators.
bitand - Bit-wise AND.
bitcmp - Complement bits.
bitor - Bit-wise OR.
bitxor - Bit-wise XOR.
bitset - Set bit.
bitget - Get bit.
bitshift - Bit-wise shift.
Set operators.
union - Set union.
unique - Set unique.
intersect - Set intersection.
setdiff - Set difference.
setxor - Set exclusive-or.
allunique - True for sets with all unique members.
ismember - True for set member.
numunique - Number of unique set members.
See also function_handle.
Elementary math functions
help elfun
Elementary math functions.
Trigonometric.
sin - Sine.
sind - Sine of argument in degrees.
sinh - Hyperbolic sine.
asin - Inverse sine.
asind - Inverse sine, result in degrees.
asinh - Inverse hyperbolic sine.
cos - Cosine.
cosd - Cosine of argument in degrees.
cosh - Hyperbolic cosine.
acos - Inverse cosine.
acosd - Inverse cosine, result in degrees.
acosh - Inverse hyperbolic cosine.
tan - Tangent.
tand - Tangent of argument in degrees.
tanh - Hyperbolic tangent.
atan - Inverse tangent.
atand - Inverse tangent, result in degrees.
atan2 - Four quadrant inverse tangent.
atan2d - Four quadrant inverse tangent, result in degrees.
atanh - Inverse hyperbolic tangent.
sec - Secant.
secd - Secant of argument in degrees.
sech - Hyperbolic secant.
asec - Inverse secant.
asecd - Inverse secant, result in degrees.
asech - Inverse hyperbolic secant.
csc - Cosecant.
cscd - Cosecant of argument in degrees.
csch - Hyperbolic cosecant.
acsc - Inverse cosecant.
acscd - Inverse cosecant, result in degrees.
acsch - Inverse hyperbolic cosecant.
cot - Cotangent.
cotd - Cotangent of argument in degrees.
coth - Hyperbolic cotangent.
acot - Inverse cotangent.
acotd - Inverse cotangent, result in degrees.
acoth - Inverse hyperbolic cotangent.
hypot - Square root of sum of squares.
deg2rad - Convert angles from degrees to radians.
rad2deg - Convert angles from radians to degrees.
Exponential.
exp - Exponential.
expm1 - Compute exp(x)-1 accurately.
log - Natural logarithm.
log1p - Compute log(1+x) accurately.
log10 - Common (base 10) logarithm.
log2 - Base 2 logarithm and dissect floating point number.
pow2 - Base 2 power and scale floating point number.
realpow - Power that will error out on complex result.
reallog - Natural logarithm of real number.
realsqrt - Square root of number greater than or equal to zero.
sqrt - Square root.
nthroot - Real n-th root of real numbers.
nextpow2 - Next higher power of 2.
Complex.
abs - Absolute value.
angle - Phase angle.
complex - Construct complex data from real and imaginary parts.
conj - Complex conjugate.
imag - Complex imaginary part.
real - Complex real part.
unwrap - Unwrap phase angle.
isreal - True for real array.
cplxpair - Sort numbers into complex conjugate pairs.
Rounding and remainder.
fix - Round towards zero.
floor - Round towards minus infinity.
ceil - Round towards plus infinity.
round - Round towards nearest integer.
mod - Modulus (signed remainder after division).
rem - Remainder after division.
sign - Signum.
Specialized math functions
help specfun
Specialized math functions.
Specialized math functions.
airy - Airy functions.
besselj - Bessel function of the first kind.
bessely - Bessel function of the second kind.
besselh - Bessel functions of the third kind (Hankel function).
besseli - Modified Bessel function of the first kind.
besselk - Modified Bessel function of the second kind.
beta - Beta function.
betainc - Incomplete beta function.
betaincinv - Inverse incomplete beta function.
betaln - Logarithm of beta function.
ellipj - Jacobi elliptic functions.
ellipke - Complete elliptic integral.
erf - Error function.
erfc - Complementary error function.
erfcx - Scaled complementary error function.
erfinv - Inverse error function.
erfcinv - Inverse complementary error function.
expint - Exponential integral function.
gamma - Gamma function.
gammainc - Incomplete gamma function.
gammaincinv - Inverse incomplete gamma function.
gammaln - Logarithm of gamma function.
psi - Psi (polygamma) function.
legendre - Associated Legendre function.
cross - Vector cross product.
dot - Vector dot product.
Number theoretic functions.
factor - Prime factors.
isprime - True for prime numbers.
primes - Generate list of prime numbers.
gcd - Greatest common divisor.
lcm - Least common multiple.
rat - Rational approximation.
rats - Rational output.
perms - All possible permutations.
nchoosek - All combinations of N elements taken K at a time.
factorial - Factorial function.
Coordinate transforms.
cart2sph - Transform Cartesian to spherical coordinates.
cart2pol - Transform Cartesian to polar coordinates.
pol2cart - Transform polar to Cartesian coordinates.
sph2cart - Transform spherical to Cartesian coordinates.
hsv2rgb - Convert hue-saturation-value colors to red-green-blue.
rgb2hsv - Convert red-green-blue colors to hue-saturation-value.
File input/output
help iofun
Spreadsheet IO Functions (Not Recommended)
xlsread - (Not recommended) Read spreadsheet file
xlswrite - (Not recommended) Write spreadsheet file
xlsfinfo - (Not recommended) Determine if file contains Microsoft Excel spreadsheet
Contents of text/iofun (Not Recommended)
csvread - (Not recommended) Read comma-separated value (CSV) file.
csvwrite - (Not recommended) Write comma-separated value file.
dlmread - (Not recommended) Read ASCII-delimited file of numeric data into matrix.
dlmwrite - (Not recommended) Write matrix to ASCII-delimited file.
textread - (Not Recommended) Read data from text file; write to multiple outputs.
Contents of tabular/iofun:
Import/Export Functions
readtable - Create table from file.
readtimetable - Create timetable from file.
readmatrix - Read matrix from file.
readcell - Create cell array from file.
readvars - Read variables from file.
writetable - Write table to file.
writetimetable - Write timetable to file.
writematrix - Write a matrix to a file.
writecell - Write cell array to file.
writelines - Write text to file.
Import Options
detectImportOptions - Create import options based on file content
delimitedTextImportOptions - Import options object for delimited text files
fixedWidthImportOptions - Import options object for fixed-width text files
spreadsheetImportOptions - Import options object for Spreadsheet files
xmlImportOptions - Import options object for XML files
htmlImportOptions - Import options object for HTML files
wordDocumentImportOptions - Import options object for Microsoft Word document files
Contents of matlab/iofun:
Import Functions
daqread - Read Data Acquisition Toolbox (.daq) data file.
importdata - Load data from file.
matfile - Save and load parts of variables in MAT-files.
matfinfo - Text description of MAT-file contents.
Internet Services
sendmail - Send e-mail.
urlread - Download URL content to character vector. (not recommended)
urlwrite - Download URL content and save to file. (not recommended)
callSoapService - Send a SOAP message off to an endpoint.
createClassFromWsdl - Create a MATLAB object based on a WSDL-file.
createSoapMessage - Create a SOAP message, ready to send to the server.
parseSoapResponse - Convert the response from a SOAP server into MATLAB types.
Path and Configuration
matlabroot - Root directory of MATLAB installation.
deployprefdir - Get the MATLAB preferences directory for a deployed component.
prefdir - Preference directory name.
partialpath - Partial pathnames.
pathsep - Path separator for this platform.
Command Window
home - Send the cursor home.
clc - Clear command window.
Time and dates
help timefun
Timing functions.
cputime - CPU time in seconds.
tic - Start stopwatch timer.
toc - Stop stopwatch timer.
etime - Elapsed time.
pause - Wait in seconds.
MATLAB as calculator
This is the simplest way of using it: evaluating numerical expressions.
Suppose we want to evaluate the numerical expression
Simply type the following code in the Command Window and then press the "Enter/Return" key (or run the current section of this live script)
4 + sqrt(2) - sin(pi/5)^2 + exp(2)
The result is assigned to the predefined variable ans.
If you compare, for example, the current code with a Python equivalent piece of code, they are quite similar;
Arithmetic operations
The most common arithmetic operations in MATLAB are
- Addition
a+b - Subtraction
- Multiplication
- Division or
- Powers
This is just like on a calculator, in spreadsheets (Excel) and most programming languages.
Order of Operations
In MATLAB (as many other programming languages) operations are performed in the following order:
- expressions in brackets: ( ) ;
- powers: ^ ;
- multiplication and division: * , / ;
- addition and subtraction: + , - .
Operations of the same precedence, for example multiplication and division, are evaluated from left to right.
In ordinary written mathematics we sometimes leave out brackets and rely on the fact that an intelligent human will understand where they ought to go. In contrast, computers obey exactly the rules for evaluating expressions. If you are unsure, adding some extra brackets (parentheses) will not hurt.
A few Examples
1+2*3 % Which operation has higher precedence?
Remember that operations of the same precedence are evaluated left to right:
24/2/3 % The same result as the the second case.
24/(2*3) % This version is usually clearer.
A final example:
5^(4^3) % Note the different result!
(5^4)^3 % This is the same as the first case, but clearer.
Changing the Displayed Format
By default, MATLAB displays 5 decimal digits, unless the number is too big or too small, when it switches to scientific notation. The format of the answers displayed in the command window can be changed using the format command. help format
format - Set output display format
This MATLAB function changes the output display format to the format
specified by style.
Syntax
format(style)
fmt = format
fmt = format(style)
Input Arguments
style - Format to apply
character vector | string scalar | DisplayFormatOptions object
Output Arguments
fmt - Current display format
DisplayFormatOptions object
Examples
Long Format
Hexadecimal Format
Short and Long Engineering Notation
Large Data Range Format
Reset Format to Default
Get Current Format
Save and Restore Display Format
See also DisplayFormatOptions, disp, fprintf, formattedDisplayText
Introduced in MATLAB before R2006a
Documentation for format
Pay attention: format does NOT affect how numbers are stored or calculations are done in MATLAB. It only affects how numbers are displayed.
A Simple Example
x = 3 + 11/16 + 2^1.2
x = 5.98489670999407e+000
Scientific Notation
For very large numbers or very small numbers it is more convenient to express the number in scientific notation using a power of 10.
3.6e+12
ans = 3.600000000000000e+12
5.2e-9
ans = 5.200000000000000e-09
2^30
ans = 1.073741824000000e+09
2^(-40)
ans = 9.094947017729282e-13
0.7/0.1 -7 % Sometimes the result may not be what you expect.
ans = -8.881784197001252e-16
Complex Numbers
MATLAB allows and works with complex numbers. All arithmetic with complex numbers works in the usual way.
You may use both i and j to denote the imaginary unit, if you did not already define any variable named i or j(see below how to set valid variable names).
Example
Define the complex number 
2+3*1i
ans = 2.000000000000000 + 3.000000000000000i
2+3i
ans = 2.000000000000000 + 3.000000000000000i
2+3j % Any of these three expression works.
ans = 2.000000000000000 + 3.000000000000000i
Define the complex expression
Special functions for complex numbers
A MATLAB function to create a complex number: create the complex number complex(2, 3) % the 1st argument is the real part, the 2nd argument is the imaginary part
ans = 2.000000000000000 + 3.000000000000000i
A MATLAB function to get the real part of the complex number A MATLAB function to get the imaginary part of the complex number A MATLAB function to get the modulus of the complex number 
A MATLAB function to get the argument of a complex number (in radians)
rad2deg(angle((2+3i)/(4+6i)))
Special Values for Infinity and for Undefined Operations
MATLAB uses the IEEE standard 754 for floating point numbers, to provide approximations to the real numbers. This standard, which is used in virtually every current computer microprocessor, specifies how floating point numbers are stored and also includes special values for infinity and for undefined operations.
Infinity (Inf)
Operations that would result in a mathematical infinity give a result of Inf, while those that would result in minus infinity give -Inf.
Not a Number (NaN)
Operations whose value cannot be mathematically determined result in a Not a Number.
Propagation of Inf and NaN in Calculations
Both Inf and Nan propagate in calculations without producing any error message.
Operations involving Inf and/or NaN are also significantly slower than those using standard floating point numbers.
Operations involving Inf may occasionally produce a NaN.
Once you have produced a NaN, it affects all calculations from then on:
Variables
Variables are essential to store the result of a calculation so it can be subsequently used in a later calculation. This not only makes your programs much more efficient, but also makes them much easier to understand.
Variable Names
A variable name is a sequence of letters, numbers and underscores "_", starting with a letter.
The following are invalid variable names. Try to insert one of those variable name in the code box below, run the section and see what message you will obtain
% insert one of the two invalid variable declaration here and see the
% resulting error message
Then insert one of the following valid variable names
You should obtain a different error message: indeed the variable name is valid, but the variable does not exist in the Matlab Workspace.
Length of variable names: although a variable name may have any length, MATLAB only recognizes the first "few" characters. How many characters are recognized is specified by the Matlab command namelengthmax (which is typically 63).
Warnings
- MATLAB is case sensitive; x and X are different variables!
- You should not use a variable name that clashes with a constant, for example pi, or with a MATLAB command, as var (Hint: help var )
- Names cannot be MATLAB keywords, for example for, if, end, etc.
Assigning Values to Variables
Matlab uses = to assign a value to a variable.
Note: the left-hand-side of the = must be a valid variable name, while the right-hand-side must be a valid expression.
x1 = (-b + sqrt(delta))/(2*a)
x2 = (-b - sqrt(delta))/(2*a)
Suppressing output
When Matlab does a calculation and assigns the result to a variable, the result is echoed to the command window.
Sometimes, especially when dealing with large vectors or matrices, it is very useful to keep the screen uncluttered by unwanted output. This is simply done by adding a semicolon ; to the end of the command
Useful Commands
There are several useful commands that allow you to see what variables you have created and if necessary remove some or all of them.
Please remember, you can always get more information on a command using the help command.
List of the Variables
- to list all the variables in the current MATLAB workspace
who x* % This command lists all the variables starting with the (lower case) letter x.
- to lists the variables, but obtaining extra information about their size and data type
Clearing Variables
To remove a variable, use the clear command
Predefined Constants
When you start MATLAB, some variables already have predefined values:
- the imaginary unit of complex numbers
or 
- the largest double precision number and the smallest positive double precision number
realmax % the largest double precision number
4*realmax % What did you expect as the result?
realmin % the smallest positive double precision number
MATLAB uses IEEE standard 754 double precision to store floating point numbers which approximate the real numbers. The characteristics of double precision arithmetic are described by the relative machine precision, also known as the machine epsilon: eps returns 
, which is the distance from 1.0 to the next larger double-precision number For more details, refer to
Caveat
You can give these variables new values. If you do so you may get strange effects afterwards!
Summary
Using this live script you have:
- seen how arithmetic expressions are evaluated in MATLAB and how to use brackets to get the desired result or make an expression clearer;
- learned how to enter numbers using scientific notation;
- learned how to change the format of the result displayed in the MATLAB Command Window;
- learned how to enter complex numbers and how to find real and imaginary parts;
- learned about Inf (infinity) and NaN (Not a Number);
- learned what are valid names for variables in MATLAB;
- learned how assign values to variables using the = operator;
- learned how to display the value of a variable;
- learned how to see what variables have been defined and how to clear a variable from your workspace.
Back to the Index
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Use this link to go back to the previous live script of this collection (Part 1).
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