# More matrix algebra: Manipulating matrices

## Abstract

The simple regression model can be expressed using vector algebra. However, in order to understand fully the multiple regression model, it is necessary to employ matrix algebra. Indeed, a basic familiarity with matrix algebra is also essential to understanding most of the techniques of multivariate statistical analysis. Matrices are simply rectangular arrays of elements. Consider, for example, the matrix G as follows:
$$G = \left[ {\begin{array}{*{20}c} {g_{11} {\mathbf{ }}g_{12} {\mathbf{ }}g_{13} } \\ {g_{21} {\mathbf{ }}g_{22} {\mathbf{ }}g_{23} } \\ \end{array} } \right]$$

This matrix is said to be “2 by 3” because it comprises two rows and three columns (i.e., 2 × 3). Each of the elements in this matrix, gy, has two subscripts. The first subscript refers to the row of the matrix in which an element appears and the second subscript refers to the column of the matrix in which it appears. For example, the element g23 is in the second row and third column of this matrix.

## Keywords

Multiple Regression Model Matrix Algebra Simple Regression Model Basic Familiarity
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