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[
]
⋅
−
−
⋅
=
⋅
⋅
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
Finally,
x
⋅
A
⋅
x
T
= 2X
2
+4Y
2
-Z
2
+6XY+2XZ+7ZY
The QUADF menu
The HP 49 G calculator provides the QUADF menu for operations related to
QUADratic Forms. The QUADF menu is accessed through
„Ø
.
This menu includes functions AXQ, CHOLESKY, GAUSS, QXA, and
SYLVESTER.
Function AXQ
In RPN mode, function AXQ produces the quadratic form corresponding to a
matrix
A
n
×
n
in stack level 2 using the
n
variables in a vector placed in stack
level 1. Function returns the quadratic form in stack level 1 and the vector of
variables in stack level 1. For example,
[[2,1,-1],[5,4,2],[3,5,-1]]
`
['X','Y','Z']
`
AXQ
returns
2: ‘2*X^2+(6*Y+2*Z)*X+4*Y^2+7*Z*y-Z^2’
1: [‘X’ ‘Y’ ‘Z’]
