Matrix Quadratic Forms; Function Qr; The Quadf Menu - HP 50g User Manual

Function QR

In RPN, function QR produces the QR factorization of a matrix A
Q orthogonal matrix, a R
n n
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
T
from x A x . For example, if we use A = [[2,1,–1][5,4,2][3,5,–1]], and x =
T
[X Y Z] , the corresponding quadratic form is calculated as
Finally,

The QUADF menu

The calculator provides the QUADF menu for operations related to QUADratic
Forms. The QUADF menu is accessed through „Ø.
n m
T
x A x X
X Y
T
x A x = 2X
upper trapezoidal matrix, and a P
2 1
⎡
⎢
Y Z 5 4
⎢
⎢
3 5
⎣
2 X Y
⎡
⎢
Z 5 X 4 Y
⎢
⎢
3 X 5 Y
⎣
2 2 2
+4Y -Z +6XY+2XZ+7ZY
returning a
n m
m m
1 X
⎤ ⎡ ⎤
⎥ ⎢ ⎥
2 Y
⎥ ⎢ ⎥
⎥ ⎢ ⎥
1 Z
⎦ ⎣ ⎦
Z
⎤
⎥
2 Z
⎥
⎥
Z
⎦
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