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
z1
7
and
z2=2eⅈπ
z2
2
e
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
zz is a complex number.
Manipulating complex numbers
| |
m-file |
| Re(zz) |
real(z) |
| Im(zz) |
imag(z) |
| |z|z |
abs(z) |
| Angle(zz) |
angle(z) |
| 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.
Common matrix operations
| Operation |
m-file |
| MNMN |
M*N |
| M-1M-1 |
inv(M) |
| MTMT |
M' |
| det(MM) |
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
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
12121212= 1 1 1 1
12
12
12
12
1
1
1
1
.
Example 2
Given a vector x, compute a vector y having elements
yn=1sinxn
yn
1
xn
.
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".