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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']
`
XQ
returns
2: ‘2*X^2+(6*Y+2*Z)*X+4*Y^2+7*Z*y-Z^2’
1: [‘X’ ‘Y’ ‘Z’]
Function QXA
Function QXA takes as arguments a quadratic form in stack level 2 and a vector
of variables in stack level 1, returning the square matrix
A
from which the
quadratic form is derived in stack level 2, and the list of variables in stack level
1. For example,
'X^2+Y^2-Z^2+4*X*Y-16*X*Z'
`
['X','Y','Z']
`
QX
returns
2: [[1 2 –8][2 1 0][-8 0 –1]]
1: [‘X’ ‘Y’ ‘Z’]
Diagonal representation of a quadratic form
Given a symmetric square matrix
A
, it is possible to “diagonalize” the matrix
A
by finding an orthogonal matrix
P
such that
P
T
⋅
A
⋅
P
=
D
, where
D
is a diagonal
matrix. If Q =
x
⋅
A
⋅
x
T
is a quadratic form based on
A
, it is possible to write
the quadratic form Q so that it only contains square terms from a variable
y
,
Summary of Contents for 50G
Page 1: ...HP g graphing calculator user s guide H Edition 1 HP part number F2229AA 90006 ...
Page 130: ...Page 2 70 The CMDS CoMmanDS menu activated within the Equation Writer i e O L CMDS ...
Page 206: ...Page 5 29 LIN LNCOLLECT POWEREXPAND SIMPLIFY ...
Page 257: ...Page 7 20 ...
Page 383: ...Page 11 56 Function KER Function MKISOM ...
Page 715: ...Page 21 68 Whereas using RPL there is no problem when loading this program in algebraic mode ...
Page 858: ...Page L 5 ...