HP 48g Graphing Calculator - Manual (Page 185)

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:
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Matrices and Linear Algebra 14-21