MATLAB Programming/Simple matrix manipulation

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Contents 1 Operations 1.1 Squaring a matrix 1.2 Determinant 1.2.1 Symbolic Determinant 1.3 Transpose 2 Systems of linear equations 2.1 Homogeneous Solutions 2.2 Particular Solutions 2.3 State Space Equations 3 Special Matrices 3.1 Identity matrix 3.2 Ones Matrix 3.3 Zero matrix

[edit] Operations

[edit] Squaring a matrix

a=[1 2;3 4];
a^2;

a^2 is the equivalent of a*a. To square each element:

a.^2

The period before the operator tells MATLAB to perform the operation element by element.

[edit] Determinant

Getting the determinant of a matrix, requires that you first define your matrix, then run the function "det()" on that matrix, as follows:

a = [1 2; 3 4];
det(a)
ans = -2

[edit] Symbolic Determinant

You can get the symbolic version of the determinant matrix by declaring the values within the matrix as symbolic as follows:

m00 = sym('m00'); m01 = sym('m01'); m10 = sym('m10'); m11 = sym('m11');

or

syms m00 m01 m10 m11;

Then construct your matrix out of the symbolic values:

m = [m00 m01; m10 m11];

Now ask for the determinant:

det(m)
ans = m00*m11-m01*m10

[edit] Transpose

To find the transpose of a matrix all you do is place a apostrophe after the bracket. Transpose- switch the rows and columns of a matrix.

Example:

a=[1 2 3]

aTranspose=[1 2 3]'

or

b=a' %this will make b the transpose of a

when a is complex, the apostrophe means transpose and conjugate.

Example a=[1 2i;3i 4]; a'=[1 -3i;-2i 4];

For a pure transpose, use .' instead of apostrophe.

[edit] Systems of linear equations

Ther are lots of ways to solve these equations.

[edit] Homogeneous Solutions

[edit] Particular Solutions

[edit] State Space Equations

[edit] Special Matrices

Often in MATLAB it is necessary to use different types of unique matrices to solve problems.

[edit] Identity matrix

To create an identity matrix (ones along the diagonal and zeroes elsewhere) use the MATLAB command "eye":

>>a = eye(4,3)
a =
   1   0   0
   0   1   0
   0   0   1
   0   0   0

[edit] Ones Matrix

To create a matrix of all ones use the MATLAB command "ones"

a=ones(4,3)

Produces:

a =

    1     1     1
    1     1     1
    1     1     1
    1     1     1

[edit] Zero matrix

The "zeros" function produces an array of zeros of a given size. For example,

a=zeros(4,3)

Produces:

a =

    0     0     0
    0     0     0
    0     0     0 
    0     0     0

This type of matrix, like the ones matrix, is often useful as a "background", on which to place other values, so that all values in the matrix except for those at certain indices are zero.