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)`
M^T	`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)=

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".