Basic operations in MATLAB
1.3
2006/02/20 13:57:47 US/Central
2006/02/21 23:21:44.061 US/Central
Anders
Gjendemsjø
gjendems@NO-SPAM.iet.ntnu.no
Darryl
Morrell
morrell@asu.edu
Darryl
Morrell
morrell@asu.edu
Basic operations
MATLAB
This module covers basic operations in MATLAB.
Basic Operations on Numbers
MATLAB has many
arithmetic operations and functions built in. Most of them are
straightforward to use. The Table below lists some commonly used
scalar operations; in this table, x and y are scalars. (A scalar is a single number.)
Common scalar mathematical operations in MATLAB
Operation
MATLAB
xy
x-y
xy
x+y
xy
x*y
xy
x/y
xy
x^y
ex
exp(x)
log10x
log10(x)
lnx
log(x)
log2x
log2(x)
Expressions are formed from numbers, variables, and these operations. The operations have different precedences. The ^ operation has the highest precedence; ^ operations are evaluated before any other operations. Multiplication and division have the next highest precedence, and addition and subtraction have the lowest precedence. Precedence is altered by parentheses; expressions within parenthesesare evaluated before expressions outside parentheses.
The Table below shows several mathematical formulas, the corresponding MATLAB expressions, and the values that MATLAB would compute for the expressions.
Example MATLAB Expressions
formula
MATLAB Expression
Computed Value
52
42
5^2+4^2
41
54
2
(5+4)^2
81
23
45
(2 + 3)/(4 - 5)
-5
log10
100
log10(100)
2
ln
4
23
log(4*(2+3))
2.9957
Basic Operations on Matrices
In addition to scalars, MATLAB can operate on matrices. Some common matrix operations are shown in the Table below; in this table, M and N are matrices.
Common matrix mathematical operations in MATLAB
Operation
MATLAB
MN
M*N
M-1
inv(M)
MT
M'
det(M)
det(M)
MATLAB functions length and size are used to
find the dimensions of vectors and matrices, respectively.
MATLAB can perform an operation on each element of a vector or matrix. To perform an arithmetic operation on each element in a vector (or matrix), rather than on the
vector (matrix) itself, then the operator should be preceded by
".", e.g .*, .^ and ./.
Let
A
1
1
1
1
.
Then A^2 will return
AA
2
2
2
2
,
while A.^2 will return
12
12
12
12
1
1
1
1
.
Given a vector x, compute a vector y having elements
yn
1
xn
.
This can be easily be done in MATLAB by typing y=1./sin(x)
Note that using / in place of ./ would result in the (common) error
Matrix dimensions must agree.
Complex numbers
MATLAB has excellent support for complex
numbers with several built-in functions available. The imaginary
unit is denoted by i or (as preferred in electrical engineering) j.
To create complex variables
z1
7
and
z2
2
e
simply enter
z1 = 7 + j and z2 = 2*exp(j*pi)
The Table below gives an overview of the basic
functions for manipulating complex numbers, where z is a complex number.
Manipulating complex numbers in MATLAB
MATLAB
Re(z)
real(z)
Im(z)
imag(z)
z
abs(z)
Angle(z)
angle(z)
z*
conj(z)
Other Useful Details
- A semicolon added at the end of a line tells MATLAB to suppress
the command output to the display.
- MATLAB Version 7 is case sensitive for both variables and functions; for example,
b and B are different variables and MATLAB will recognize the built-in function sum but not SUM. In previous versions, MATLAB was not case sensitive for function names.
- Often it is useful to split a statement over multiple lines. To split a
statement across multiple lines, enter three periods
... at the end of
the line to indicate it continues on the next line.
Splitting
y
a
b
c
over multiple lines.
y = a...
+ b...
c;