MATLAB can be used to work with matrices, perform mathematical operations, generate random numbers, and create script and function files. Key features include storing variables and matrices, indexing matrix elements, performing operations on real and complex numbers, and using functions like sum, diag, and random number generators. Help commands provide documentation on elementary, advanced, and matrix functions in MATLAB. M-files allow storing and running scripts and functions.

1. MATLAB
Basic MATLAB -
matrices
operators
script and function files
flow control
plotting
Basic MATLAB
optional windows
workspace
current directory
s here
command window
Screen shot of the Matlab window
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2. MATLAB Variables
all variables stored in 32bit floating point format
no distinction between real and integer
>>a = 3;
same assignment for “a”
>>a = 3.0;
Matlab is case sensitive
>>A=3;
A≠a
>>a=2;
MATLAB Variables
can use numbers and underscore in variable names
>>case34=6.45;
OK
>>case_34=6.45;
names must start with a letter
>>34case=23.45; syntax error
string (text) variables enclosed in single quotes.
The variable is stored as array of characters
>>title=‘This is the title’;
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3. MATLAB Variables
if a variable is defined,
typing the variable name returns its value
>>a=45.57;
>>a
a=
45.57
to clear a variable from memory
>>a=4
>>clear a
MATLAB Variables
Matlab will “echo” commands unless a semi-
colon is used
>>a=23.2;
>>
>>a=23.2
a= Matlab echoes the command
23.2
>>
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4. MATLAB Variables
Vectors
column vectors row vectors
⎧1 ⎫
⎪ ⎪
a = ⎨2 ⎬ a = {1 2 3}
⎪3 ⎪
⎩ ⎭
>>a=[1;2;3]; >>a=[1,2,3];
>>a >>a
a= a=
1 1 2 3
2
3 use comma
use semi-colon
to separate rows to separate columns
MATLAB Variables
Matrices
⎡1 2 3⎤
2-dimensional matrices a=⎢ ⎥
⎣4 5 6⎦
>>a=[1,2,3;4,5,6];
>>a
a=
1 2 3
4 5 6
again, separate columns with commas and rows
with semi-colons
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5. MATLAB Variables
Indexing Matrix elements
A vector is a special type of matrix
row vector is a 1 x n matrix, 1 row n columns
column vector is a n x 1 matrix, n rows 1 column
>>a=[1,2,3];
>>a(2) could also reference by a(1,2)
ans = note, a(2,1) would produce an error
2 because “a” only has one row
MATLAB Variables
Indexing Matrix elements
more examples
⎡1 2 3⎤ >>a=[1,2,3;4,5,6];
a=⎢ ⎥
⎣4 5 6⎦
assigning
addressing
>>a(2,2)=9;
>>a(2,3) >>a
ans = a=
6 1 2 3
4 9 6
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6. MATLAB Variables
Complex-valued numbers
Typically, the variable “i” or “j” is used to
represent the complex variable; e.g.
i = −1
Then, a complex number is represented as
z = a + ib Re(z) = a
Im(z) = b
MATLAB Variables
Complex-valued numbers
Unless i or j has been previously defined, Matlab
assigns i and j the complex variable value
In Matlab, a complex variable is represented in the
following format
>>z=23+i*56; >>z=23+j*56;
>>z >>z
z= z=
23.00 + 56.00i 23.00 + 56.00i
Matlab always uses the symbol “i” to represent a
complex number
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7. MATLAB Operations
Basic operations
addition +
subtraction -
multiplication *
division
right division /
left division ?
>>a=3;b=4; c1=0.75
>>c1=a/b; so, be careful!
c2=1.3333….
>>c2=ab;
MATLAB Operations
Mixed Real and Complex valued Variables
if both variables are real-valued, a real-valued result
is obtained
if one variable is complex-valued, Matlab recasts
the real variable as complex and then performs the
operation. The result is complex-valued
however, the type casting is done internally, the
real-valued variable remains real after the operation
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8. MATLAB Operations
Other (Scalar) Operations
Math representation Matlab interpretation
z = yx >>z=y^x;
y = ex >>y=exp(x);
y = ln(x) >>y=log(x);
y = log(x) >>y=log10(x)
y = sin(x) y = sin −1 (x) >>y=sin(x); >>y=asin(x);
y = cos(x) y = cos −1 (x) >>y=cos(x); >>y=acos(x);
y = tan(x) y = tan −1 (x) >>y=tan(x); >>y=atan(x);
MATLAB Operations
Matrices
Only matrices of the same dimension can be added and subtracted
For multiplication, the inner dimensions must be the same
⎡4 5⎤
⎡1 2 3⎤ ⎡2 3 4⎤
A=⎢ ⎥ B=⎢ ⎥ C = ⎢6 7 ⎥
⎣4 5 6⎦ ⎢ ⎥
⎣5 6 7 ⎦ ⎢8 9 ⎥
⎣ ⎦
No error Error
>>D=A+B; >>D=A+C;
>>D=A-B; >>D=A*B;
>>D=A*C; Matrix multiplication >>D=B*A;
>>D=C*A; not commutative
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9. MATLAB Operations
Left() and Right(/) Matrix “division”
Math representation Matlab interpretation
C = A −1B >>C=AB;
C = BA −1 >>C=B/A;
Remember, A must be square and
full rank (linearly independent
rows/columns)
MATLAB Operations
Matrix Transpose
Math representation Matlab interpretation
C = AT >>C=A’;
For complex-valued matrices, complex conjugate transpose
⎡1 2 3⎤
A=⎢ ⎥ a = [1 + j2 3 + j4]
⎣4 5 6⎦
>>B=A’; >>b=a’;
⎡1 4 ⎤
B = ⎢2 5⎥ ⎡1 − j2 ⎤
⎢ ⎥ b=⎢ ⎥
⎢3 6⎥
⎣ ⎦ ⎣3 − j4 ⎦
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10. MATLAB Operations
Concatenation
MATLAB Operations
Deleting Rown and Columns
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11. MATLAB Operations
The ‘.’ operator
.* does element by element multiplication
./ and . : Element by element left and right
division respectavely
MATLAB Operations
The COLON operator :
The expression 1:10
is a row vector containing numbers 1 to 10
1 2 3 …… 10
To obtain non unit spacing , specify an increment
For Example 1:2:10 gives
1 3 5 7 9
Subscript expressions involving ‘:’ refer to a part of a
matrix
A(1:k,j) is the first k elements of the jth column of A
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12. MATLAB Operations
Some other useful functions :
The sum function : Returns a row vector containing
sum of all elements in each column.
sum(A)
ans =
34 34 34 34
The diag function : Returns a row vector containing
the principal diagonal elements
Diag (A)
ans =
16 10 7 1
MATLAB Operations
The Random number generators
Rand : Generates random numbers following a
uniform distribution
Randn : Generates random numbers following a
normal distribution (mean 0 ,variance=1 , sd =1 )
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13. MATLAB Operations
Some Key Help commands
Help elfun : Elementary mathematical functions
Help specfun: Advanced mathematical functions
Help elmat: Advanced matrix functions
MATLAB m-files
Two types of m-files
script files
collection of commands that Matlab executes
when the script is “run”
function files
collection of commands which together
represent a function, a procedure or a method
Both types are separate files with a “.m” extension
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14. MATLAB m-files
To create an m-file, open the Matlab text editor
Click on the “page” icon
The Matlab text editor window will open
MATLAB m-files
Script Files
On the command line In the script file named test.m
>>x=3.0;
>>y=x^2;
>>y
y =
9.0
>>
On the command line
>>test
y =
9.0
>>
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15. MATLAB m-files
Script Files
script files share the workspace memory
test.m script
>>x=5.0;
>>test
>>y
y =
25.0
>>
MATLAB m-files
Script Files
script files can call other script files
inner.m script
>>outter
y = outter.m script
36.0
>>
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16. MATLAB m-files
Function Files
Matlab identifies function files from script files by
using the “function” and “return” keywords
Syntax: function [list of outputs] = filename (inputs)
the name of the function file must be
the same name as the function
MATLAB m-files
Function Files
The function file x2.m
>>r=3; >>h=x2(4.2);
>>d=x2(r); >>h
>>d h =
d = 17.64
9.0 >>
>>
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17. MATLAB m-files
Function Files
Multiple Inputs and Outputs
outputs in square brackets, [ ] inputs in parentheses ( )
MATLAB m-files
Function Files
variables created in the function are not
retained in the workspace, except for the
output variables
the function does not have access to
workspace variables, except for the inputs
variables passed to the function are “copies” of the
workspace variables. Changing their value inside
the function has no effect on their value in the
workspace.
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18. MATLAB Flow Control
The “while” and “if” statements
while expression if expression if expression
statements statements statements1
end end else
statements2
end
Matlab evaluates expression as logical “true” or “false”
“false” equivalent to zero
“true” equivalent to any non-zero number
statements, any valid Matlab command
MATLAB Flow Control
evaluating expression
any valid equation conditional operators
a=4; == equal to
b=5; < less than
c=5; > greater than
if a+b “True” <= less than or equal to
if b-c “False” >= greater than or equal to
watch out for round-off ~= not equal to
and word length error logical operators
if sin(0) “False” & and
if sin(pi) “True” | or
sin(pi) = 1.22e-16 while(3<=a)&(a<=5)
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19. MATLAB Flow Control
The “for” statement
for index = start : [increment :] end
statements
end
increment is optional, if increment is not specified
increment defaults to 1
index, start, increment, and end do not need to be integer
valued
index can be incremented positive (increment > 0)
or negative (increment < 0)
loop stops when index > end (or index < end)
MATLAB Flow Control
example
script file to cycle through x values
function file to generate the y values
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20. MATLAB Plotting
Basic 2D plotting functions
plot(x1,y1[,x2,y2,x3,y3.....])
xlabel(‘x axis name’)
ylabel(‘y axis name’)
title(‘graph name’)
Additional functions
grid on
grid off
axis([xmin,xmax,ymin,ymax])
MATLAB Plotting
example y = sin(t)
the “plot” function alone
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21. MATLAB Plotting
example y = sin(t)
script file to generate
a graph of y = sin(t)
MATLAB Plotting
example y = sin(t)
function file to generate
a graph of y = sin(t)
>>graphsin
>>
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22. MATLAB Plotting
Adding a Legend for multiple graphs
“legend” remembers
the order the graphs
were plotted
MATLAB Plotting
Plot function in some detail
•PLOT(X,Y) plots vector Y versus vector X
•If X is a scalar and Y is a vector, length(Y) disconnected
points are plotted.
•If Y is complex, PLOT(Y) is equivalent to PLOT
(real(Y),imag(Y)).
Additional functions
grid on
grid off
axis([xmin,xmax,ymin,ymax])
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23. b blue . point - solid
g green o circle : dotted
r red x x-mark -. dashdot
c cyan + plus -- dashed
m magenta * star
y yellow s square
k black d diamond
v triangle (down)
^ triangle (up)
< triangle (left)
> triangle (right)
p pentagram
h hexagram
MATLAB Plotting
3D Plots
The plot3 command
Three dimensional analog of plot
where x, y and z are three vectors of the same length,
plots a line in 3D-space through the points whose
coordinates are the elements of x, y and z.
Character string can be used with the plot3 command
just as with the plot command
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24. Thank you
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