3.4: Basic Complex and Matrix Operations
Complex numbers
mfile environments have excellent support for complex numbers. The imaginary unit is denoted by
i
or
(as preferred in Electrical Engineering)
j
.
To create complex variables and simply enter
z1 = 7 + j
and
z2 = 2*exp(j*pi)
Table 2 gives an overview of the basic functions for manipulating complex numbers, where is a complex number.
mfile  

real(z) 

imag(z) 

abs(z) 

angle(z) 

conj(z) 
Operations on Matrices
In addition to scalars, mfile environments can operate on matrices. Some common matrix operations are shown in Table 3; in this table,
M
and
N
are matrices.
Operation  mfile 

M*N 

inv(M) 

M' 

det(M) 
Some useful facts:
 The functions
length
and
size
are used to find the dimensions of vectors and matrices, respectively.
 Operations can also be performed on each element of a vector or matrix by proceeding the operator by ".", e.g
.*
,
.^
and
./
.
Example 4
Let . Then
A^2
will return , while
A.^2
will return .
Example 5
Given a vector
x
,
compute a vector
y
having elements . This can be easily be done with the command
y=1./sin(x)
Note that using
/
in place of
./
would result in the (common) error "Matrix dimensions must agree".