Introduction to Matrix Algebra

Psychology 7291: Multivariate Statistics (Carey) 8/27/98 Matrix Algebra - 1 Introduction to Matrix AlgebraDefinitions:A Matrix is a collection of numbers ordered by rows and columns. It is customaryto enclose the elements of a Matrix in parentheses, brackets, or braces. For example, thefollowing is a Matrix :X = 582 107 .This Matrix has two rows and three columns, so it is referred to as a 2 by 3 Matrix . Theelements of a Matrix are numbered in the following way:X = x11x12x13x21x22x23 That is, the first subscript in a Matrix refers to the row and the second subscript refers tothe column. It is important to remember this convention when Matrix Algebra vector is a special type of Matrix that has only one row (called a row vector) orone column (called a column vector). Below, a is a column vector while b is a rowvector. a=723 ,b= 274()A scalar is a Matrix with only one row and one column.

For matrix multiplication to be legal, the first matrix must have as many columns as the second matrix has rows. This, of course, is the requirement for multiplying a row vector by a column vector. The resulting matrix will have as many rows as the first matrix and

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  Matrix, Multiplication, Multiplication matrix

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