HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 377)

100

101

Page 11-51

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 A

returning a

lower L

trapezoidal matrix, a Q

orthogonal matrix, and a P

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]]

[[-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 A

returning

a Q

orthogonal matrix, a R

upper trapezoidal matrix, and a P

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⋅x

. For example, if we use A = [[2,1,–1][5,4,2][3,5,–

1]], and x = [X Y Z]

, the corresponding quadratic form is calculated as

1 2 ... 372 373 374 375 376 377 378 379 380 381 382 ... 863 864

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HP 48gII Graphing Calculator Manual do Utilizador Página 377

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