6.1 Introduction

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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