HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 339

For square matrices of higher order determinants can be calculated by using smaller order determinant called cofactors. The general idea is to "expand" a determinant of a n×n matrix (also referred to as a n×n determinant) into a sum of the cofactors, which are (n-1)×(n-1) determinants, multiplied by the elements of a single row or column, with alternating positive and negative signs. This "expansion" is then carried to the next (lower) level, with cofactors of order (n2)×(n-2), and so on, until we are left only with a long sum of 2×2 determinants. The 2×2 determinants are then calculated through the method shown above. The method of calculating a determinant by cofactor expansion is very inefficient in the sense that it involves a number of operations that grows very fast as the size of the determinant increases. A more efficient method, and the one preferred in numerical applications, is to use a result from Gaussian elimination. The method of Gaussian elimination is used to solve systems of linear equations. Details of this method are presented in a later part of this chapter. To refer to the determinant of a matrix A, we write det(A). A singular matrix has a determinant equal to zero. Function TRACE Function TRACE calculates the trace of square matrix, defined as the sum of the elements in its main diagonal, or Examples: n ∑ tr(A) = aii . i =1 Page 11-13