22 - Introduction to matrix algebra

Abstract

This chapter describes the laws of matrix algebra by a methodological approach. A rectangular matrix can be described as a table or array of quantities, where the quantities usually take the form of numbers. A row can be described as a horizontal line of quantities, and a column can be described as a vertical line of quantities. Matrices can be multiplied together, by multiplying the rows of the pre-multiplier into the columns of the post-multiplier. A diagonal matrix is a square matrix that contains all its non-zero elements in a diagonal, from the top left corner of the matrix to its bottom right corner. A special case of diagonal matrix is where all the non-zero elements are equal to unity. This matrix is called a unit matrix, as it is the matrix equivalent to unity. The inverse or reciprocal matrix is required in matrix algebra, as it is the matrix equivalent to a scalar reciprocal, and it is used for division.