HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 377

1: [[-1.03 1.02 3.86 ][ 0 5.52 8.23 ][ 0 -1.82 5.52]] Function LQ The LQ function produces the LQ factorization of a matrix An×m returning a lower Ln×m trapezoidal matrix, a Qm×m orthogonal matrix, and a Pn×n permutation matrix, in stack levels 3, 2, and 1. The matrices A, L, Q and P are related by P⋅A = L⋅Q. (A trapezoidal matrix out of an n×m matrix is the equivalent of a triangular matrix out of an n×n matrix). For example, [[ 1, -2, 1][ 2, 1, -2][ 5, -2, 1]] LQ produces 3: [[-5.48 0 0][-1.10 -2.79 0][-1.83 1.43 0.78]] 2: [[-0.91 0.37 -0.18] [-0.36 -0.50 0.79] [-0.20 -0.78 -0.59]] 1: [[0 0 1][0 1 0][1 0 0]] Function QR In RPN, function QR produces the QR factorization of a matrix An×m returning a Qn×n orthogonal matrix, a Rn×m upper trapezoidal matrix, and a Pm×m permutation matrix, in stack levels 3, 2, and 1. The matrices A, P, Q and R are related by A⋅P = Q⋅R. For example, [[ 1,-2,1][ 2,1,-2][ 5,-2,1]] QR produces 3: [[-0.18 0.39 0.90][-0.37 -0.88 0.30][-0.91 0.28 -0.30]] 2: [[ -5.48 -0.37 1.83][ 0 2.42 -2.20][0 0 -0.90]] 1: [[1 0 0][0 0 1][0 1 0]] Note: Examples and definitions for all functions in this menu are available through the help facility in the calculator. Try these exercises in ALG mode to see the results in that mode. Matrix Quadratic Forms A quadratic form from a square matrix A is a polynomial expression originated from x⋅A⋅xT. For example, if we use A = [[2,1,-1][5,4,2][3,5,- 1]], and x = [X Y Z]T, the corresponding quadratic form is calculated as Page 11-51