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** Previous:** Simple Matrix Processing

##

Inverses, Powers and such

The following code shows how you can:
- Create an identity matrix
- Compute determinant, inverse of a matrix
- Compute powers of a matrix

A discussion of this code follows...

% Hints: use ; at end of line to prevent debug'ish output from being printed
% Matrices
A = pascal(3)
B = magic(3)
% Identity Matrices
eye(3,4); % Returns a 3 x 4 identity matrix
% Determinant -- WARNING: Round off error
d = det(A)
% Inverse of Matrix
X = inv(A)
d = det(A) % A is symmetric and has integer values -- same det
X = A^2 % Computes matrix squared
X = A.^2 % Squares each element
Y = B^(-3)
sqrt(A) % Element-based sqrt
sqrtm(A) % Matrix-based sqrt

We start with the usual test-matrix definitions. Then I have shown how you can create an identity matrix using the eye(int, int) function. This is pretty handy when you want to do scalar-vector or scalar-matrix conversions.

Then I have shown the use of det(matrix) function to compute the determinant and the use of inv(matrix) function to compute its inverse. Now that's cool, I think because usually to compute matrix inverses you end up doing a lot of processing.

Following that I have shown the use of the `' operator to compute powers of a matrix. Note that `2' (for example) is used to compute the squared-matrix whereas `.2' is used to calculate the sqaure of each individual element. Negative powers can also be computed as shown.

Another useful function is the squareroot-computing function. Again it has two variants depending on whether we want to handle individual matrix elements or the matrix as a whole.

A =
1 1 1
1 2 3
1 3 6
B =
8 1 6
3 5 7
4 9 2
d =
1
X =
3 -3 1
-3 5 -2
1 -2 1
d =
1
X =
3 6 10
6 14 25
10 25 46
X =
1 1 1
1 4 9
1 9 36
Y =
0.0053 -0.0068 0.0018
-0.0034 0.0001 0.0036
-0.0016 0.0070 -0.0051
ans =
1.0000 1.0000 1.0000
1.0000 1.4142 1.7321
1.0000 1.7321 2.4495
ans =
0.8775 0.4387 0.1937
0.4387 1.0099 0.8874
0.1937 0.8874 2.2749

** Next:** Data Analysis
** Up:** Matrix Manipulation
** Previous:** Simple Matrix Processing
Arvind Gopu
2006-03-24