Complex and Matrix Operations

Summary: This module covers basic complex and matrix operations in an m-file environment.

Complex numbers

m-file 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 z₁=7+ⅈ andz₂=2e^ⅈπ simply enter z1 = 7 + j and z2 = 2*exp(j*pi)

The table gives an overview of the basic functions for manipulating complex numbers, where z is a complex number.

TABLE 1:Manipulating complex numbers

	m-file
Re(z)	real(z)
Im(z)	imag(z)
|z|	abs(z)
Angle(z)	angle(z)
z*	conj(z)

Operations on Matrices

In addition to scalars, m-file environments can operate on matrices. Some common matrix operations are shown in the Table below; in this table, M and N are matrices.

TABLE 2: Common matrix operations

Operation	m-file
MN	M*N
M-1	inv(M)
MT	M'
det(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 1

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

).

EXAMPLE 2

Given a vector x, compute a vector y having elements y(n)=

1

sin(x(n))

 . This can be easily be done the command y=1./sin(x) Note that using / in place of ./ would result in the (common) error "Matrix dimensions must agree".