Function sylvester, Function gauss, Linear applications – HP 50g Graphing Calculator User Manual

Page 381: Function sylvester ,11-54 function gauss ,11-54, Linear applications ,11-54

Advertising
background image

Page 11-54

such that x = P

y, by using Q = xAx

T

= (P

y)⋅A⋅ (Py)

T

= y

⋅(P

T

AP)⋅y

T

=

y

Dy

T

.

Function SYLVESTER

Function SYLVESTER takes as argument a symmetric square matrix A and returns
a vector containing the diagonal terms of a diagonal matrix D, and a matrix P,
so that P

T

AP = D. For example:

[[2,1,-1],[1,4,2],[-1,2,-1]] SYLVESTER

produces

2: [ 1/2 2/7 -23/7]
1: [[2 1 –1][0 7/2 5/2][0 0 1]]

Function GAUSS

Function GAUSS returns the diagonal representation of a quadratic form Q =
x

Ax

T

taking as arguments the quadratic form in stack level 2 and the vector

of variables in stack level 1. The result of this function call is the following:

An array of coefficients representing the diagonal terms of D (stack
level 4)

A matrix P such that A = P

T

DP (stack level 3)

The diagonalized quadratic form (stack level 2)

The list of variables (stack level 1)

For example:

'X^2+Y^2-Z^2+4*X*Y-16*X*Z' `

['X','Y','Z'] ` G USS

returns

4: [1 –0.333 20.333]
3: [[1 2 –8][0 –3 16][0 0 1]]
2: ’61/3*Z^2+ -1/3*(16*Z+-3*Y)^2+(-8*z+2*Y+X)^2‘
1: [‘X’ ‘Y’ ‘Z’]

Linear Applications

The LINEAR APPLICATIONS menu is available through the „Ш.

Advertising