To decompose or factor a matrix – HP 48g Graphing Calculator User Manual
Page 185
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1. Enter the square (n x
n)
matrix onto the stack,
2,
Press f MTH ]
M f i T R
(IMXT
) E G V .
An
n x n
matrix of
eigenvectors is returned to level 2 and an »-element vector of
eigenvalues is returned to level 1. The columns of the matrix on
level 2 represent eigenvectors corresponding to the eigenvalues in
level 1.
To decompose or factor a matrix:
The HP 48 offers a set of matrix decompositions and factorizations
that you may use either alone or in programmed routines to solve
specialized problems. These factorizations are all found in the ( M T H )
M
H
T R
F f l C
T
R
menu:
LU
Crout lU Decomposition. This procedure is used
in the process of solving an exactly-determined
system of linear equations, inverting a matrix, and
computing the determinant of a square matrix. It
factors the square matrix (A) into a lower-triangular
matrix L (returned on level 3) an upper-triangular
matrix U containing ones on its diagonal (returned
on level 2), and a permutation matrix P (returned to
level 1) such that PA = LU.
L Q
LQ Factorization. This procedure factors a
rnxn
matrix A into an
m x n
lower trapezoidal matrix L
(returned to level 3), an
nxn
orthogonal matrix Q
(returned to level 2), and an
mxm
permutation
matrix P (returned to level 1) such that PA = LQ.
Q R
QR Factorization. This procedure factors a
mxn
matrix A into an
mxm
orthogonal matrix Q
(returned to level 3), an
mxn
upper trapezoidal
matrix R (returned to level 2), and an
nxn
permutation matrix P (returned to level 1) such that
AP = QR.
To compute the eigenvalues and eigenvectors for a square matrix:
14
Matrices and Linear Algebra 14-21