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
n
×
m
returning a
lower
L
n
×
m
trapezoidal matrix, a
Q
m
×
m
orthogonal matrix, and a
P
n
×
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
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]]
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
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
