Hp 49g Graphing Calculator Manual do Utilizador descarregar pdf (Página 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

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