HP 49g Graphing Calculator - Manual (Page 62)

To decompose or factor a matrix
The HP 49G offers a set of matrix decomposition and factorization tools
that you can use either alone or in program routines to solve specialized
problems. These tools are explained in the following table:
Keys Description
H
(MATRICES)
FACTORIZATION LU Grout 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, an upper-triangular matrix U
containing ones on its diagonal, and a
permutation matrix P such that
PA = LU.
R
(MATRICES)
FACTORIZATION LO LQ Factorization. This command
factors an m
x
n matrix A into an m
x
n
lower trapezoidal matrix L, an n
x
n
orthogonal matrix Q, and an m
x
m
permutation matrix P such that
PA = LQ.
(^]
(MATRICES)
FACTORIZATION OR QR Factorization. This command
factors an m
x
n matrix A into an m
x
m orthogonal matrix Q, an m
x
n upper
trapezoidal matrix R, and an n
x n
permutation matrix P such that
AP = QR.
R
(i\ilCB)
FACTORIZATION
SCHIIR
Schur Decomposition. This
command factors a square matrix A
into an orthogonal matrix Q and an
upper-triangular matrix (or, if A is real­
valued, the upper quasi-triangular
matrix) U such that A = QUQ^ (where
Q^ is the transpose of matrix Q).
Matrices and linear algebra Page 5-21