HP 48g Graphing Calculator - Manual (Page 186)

sc hi UR Schur Decomposition. This procedure factors a
square matrix A into an orthogonal matrix Q
(returned to level
2
) and an upper-triangular matrix
(or, if A is real-valued, the upper quasi-triangular
matrix) U (returned to level 1) such that: A =
QUQ"^ (Q'T is the transpose of matrix Q).
S V D Singular Value Decomposition. This procedure
factors a m x n matrix A into an m x m orthogonal
matrix U (returned to level 3), a n x n orthogonal
matrix V (returned to level 2), and a vector S of the
singular values of A such that: A = US‘V (S‘ is the
14 m x n matrix formed by using the elements of S as its
diagonal elements).
To compute the singular values of a matrix:
1. Enter the matrix onto the stack.
2. Press iMTH ) MRT.R FflCTR ( IMXT ) SVL to return a real vector
of the singular values, arranged in non-increasing order.
To recoiTstruct ;
factor mc'irices: matrix from its singular values and orthogonal
1. Enter the orthogonal matrix U onto the stack.
2. Enter the vector S.
3. Enter the demensions of the matrix { m n }.
4. Press
( M T H 1
MFiTR
( N X T )
D I to construct a matrix using the
singular values as its diagonal elements.
5. Press (3.
6
. Enter the orthogonal factor matrix (V) with the same number of
columns as the original matrix.
7. Press to recompute the original matrix. The degree to which
the recomputed matrix matches the original matrix reflects the
accuracy of the decomposition.
14-22 Matrices and Linear Algebra