6.1 Introduction


• Matrices allow simple equations that drive a large number of repetitive calculations - as a result they are found in many computer applications.


• A matrix has the form seen below,



• In Scilab,


6.1.1 Basic Matrix Operations


• Matrix operations are available for many of the basic algebraic expressions, examples are given below. There are also many restrictions - many of these are indicated.




6.1.2 Determinants

• Determinants give a ’magnitude product’ of a matrix. This can be though of as a general magnitude of the matrix.

• To find a determinant the matrix must must be square.



• For a 2 by 2 matrix.

• For a 3 by 3 matrix

• Higher order matrices follow a similar pattern. For example a 4th order matrix has the pattern,

6.1.3 Transpose


6.1.4 Adjoint Matrices


6.1.5 Inverse Matrices



• Some Scilab,


6.1.6 Identity Matrix



6.1.7 Eigenvalues


• The eigenvalue of a matrix is found using,



6.1.8 Eigenvectors