Function qr, Matrix quadratic forms, The quadf menu – HP 50g Graphing Calculator User Manual
Page 379: Function qr ,11-52, Matrix quadratic forms ,11-52, The quadf menu ,11-52
Page 11-52
Function QR
In RPN, function QR produces the QR factorization of a matrix A
n
×m
returning a
Q
n
×n
orthogonal matrix, a R
n
×m
upper trapezoidal matrix, and a P
m
×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]]
Matrix Quadratic Forms
A quadratic form from a square matrix A is a polynomial expression originated
from x
⋅A⋅x
T
. 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
Finally, x
⋅A⋅x
T
= 2X
2
+4Y
2
-Z
2
+6XY+2XZ+7ZY
The QUADF menu
The calculator provides the QUADF menu for operations related to QUADratic
Forms. The QUADF menu is accessed through „Ø.
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.
[
]
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⋅
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
⋅
=
⋅
⋅
Z
Y
X
Z
Y
X
T
1
5
3
2
4
5
1
1
2
x
A
x
[
]
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
+
+
+
−
+
⋅
=
Z
Y
X
Z
Y
X
Z
Y
X
Z
Y
X
5
3
2
4
5
2