Statistical Analysis in Forensic Science: Evidential Values of Multivariate Physicochemical Data

Appendix B

Matrices: An introduction to matrix algebra

B.1 Multiplication by a constant

Let us define matrices X and Y with i rows and j columns (i × j):

When multiplying a matrix by a constant each matrix element has to be multiplied:

Example

A matrix multiplied by a constant a = 2, gives the matrix Z:

   In order to load a matrix X and carry out multiplication by a constant, the following commands should be typed into R (Appendix D):

The output is as follows:

B.2 Adding matrices

Adding (or subtracting) matrices can be done only for matrices of the same order. When X and Y are i × j matrices, the corresponding xij and yij elements are summed (or subtracted) to give a resulting matrix Z of the same size i × j:

Example

   In R:

   The output is as follows:

The properties of ...