Transcription of Introduction to Matrix Algebra
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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).
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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