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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).

Trace of a Matrix: The trace of a matrix is sometimes, although not always, denoted as tr(A). The trace is used only for square matrices and equals the sum of the diagonal elements of the matrix. For example, tr 3 7 2-1 6 4 9 0 -5 = 3+ 6 − 5 = 4 Orthogonal Matrices:

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