Hp 48g Graphing Calculator Uživatelský manuál stáhnout pdf (Strana 186)

100

101

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 mxn matrix A into an m x m orthogonal

matrix U (returned to level 3), a nxn 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 mxn 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 (MTH 1 MFiTR (NXT) 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

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