MATLAB Programming/Advanced Topics/Numerical Manipulation/Simple matrix manipulation
Operations[edit | edit source]
Squaring a matrix[edit | edit source]
a=[1 2;3 4]; a^2;
a^2 is the equivalent of a*a. To square each element:
The period before the operator tells MATLAB to perform the operation element by element.
Determinant[edit | edit source]
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
Symbolic Determinant[edit | edit source]
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');
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
Transpose[edit | edit source]
To find the transpose of a matrix all you do is place an apostrophe after the bracket. Transpose- switch the rows and columns of a matrix.
a=[1 2 3] aTranspose=[1 2 3]'
b=a' %this will make b the transpose of a
when a is complex, the apostrophe means transpose and conjugate.
a=[1 2i;3i 4]; a'=[1 -3i;-2i 4];
For a pure transpose, use .' instead of apostrophe.
Systems of linear equations[edit | edit source]
There are lots of ways to solve these equations.
Homogeneous Solutions[edit | edit source]
Particular Solutions[edit | edit source]
State Space Equations[edit | edit source]
Special Matrices[edit | edit source]
Often in MATLAB it is necessary to use different types of unique matrices to solve problems.
Identity matrix[edit | edit source]
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
Ones Matrix[edit | edit source]
To create a matrix of all ones use the MATLAB command "ones"
a = 1 1 1 1 1 1 1 1 1 1 1 1
Zero matrix[edit | edit source]
The "zeros" function produces an array of zeros of a given size. For example,
a = 0 0 0 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.