HP (Hewlett-Packard) 50g ユーザーズマニュアル
Page 11-53
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
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,
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’]
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,
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’]
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
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,