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# Basic operations in MATLAB

Based on: Using MATLAB by Anders Gjendemsjø

Summary: This module covers basic operations in MATLAB.

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## 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.)

Table 1: Common scalar mathematical operations in MATLAB
Operation MATLAB
xyxy x-y
x+yxy x+y
xyxy x*y
xyxy x/y
xyxy x^y
exex exp(x)
log10xlog10x log10(x)
lnxlnx log(x)
log2xlog2x 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.

### Example 1

The Table below shows several mathematical formulas, the corresponding MATLAB expressions, and the values that MATLAB would compute for the expressions.

Table 2: Example MATLAB Expressions
formula MATLAB Expression Computed Value
52+42 52 42 5^2+4^2 41
5+42 54 2 (5+4)^2 81
2+345 23 45 (2 + 3)/(4 - 5) -5
log10100 log10 100 log10(100) 2
ln4×(2+3) 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.

Table 3: Common matrix mathematical operations in MATLAB
Operation MATLAB
MNMN M*N
M-1M-1 inv(M)
MTMT M'
det(MM) 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 ./.

### Example 2

Let A=( 1 1 1 1 ) A 1 1 1 1 . Then A^2 will return AA=( 2 2 2 2 ) AA 2 2 2 2 , while A.^2 will return ( 1212 1212 )=( 1 1 1 1 ) 12 12 12 12 1 1 1 1 .

### Example 3

Given a vector x, compute a vector y having elements yn=1sinxn 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+i z1 7 and z2=2eiπ 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 zz is a complex number.

Table 4: Manipulating complex numbers in MATLAB
MATLAB
Re(zz) real(z)
Im(zz) imag(z)
|z|z abs(z)
Angle(zz) angle(z)
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.

### Example 4

Splitting y=a+b+c y a b c over multiple lines.


y = a...
+ b...
c;

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