Hp 50g Graphing Calculator Manual de usuario descargar pdf (Pagina 336)

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Page 11-9

Functions RNRM and CNRM

Function RNRM returns the Row NoRM of a matrix, while function CNRM

returns the Column NoRM of a matrix. Examples,

Singular value decomposition

To understand the operation of Function SNRM, we need to introduce the

concept of matrix decomposition. Basically, matrix decomposition involves the

determination of two or more matrices that, when multiplied in a certain order

(and, perhaps, with some matrix inversion or transposition thrown in), produce

the original matrix. The Singular Value Decomposition (SVD) is such that a

rectangular matrix A

m×n

is written as A

m×n

= U

m×m

⋅S

m×n

⋅V

n×n

where U and V are orthogonal matrices, and S is a diagonal matrix. The

diagonal elements of S are called the singular values

of A and are usually

ordered so that s

≥ s

i+1

, for i = 1, 2, …, n-1. The columns [u

] of U and [v

] of

V are the corresponding singular vectors. (Orthogonal matrices

are such that

U⋅ U

= I. A diagonal matrix has non-zero elements only along its main

diagonal).

The rank of a matrix can be determined from its SVD by counting the number of

non-singular values. Examples of SVD will be presented in a subsequent

section.

Row norm and column norm of a matrix

The row norm of a matrix is calculated by taking the sums of the absolute values

of all elements in each row, and then, selecting the maximum of these sums.

The column norm of a matrix is calculated by taking the sums of the absolute

values of all elements in each column, and then, selecting the maximum of these

sums.

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Hp 50g Graphing Calculator Manual de usuario Pagina 336

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