HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 336)

100

101

Page 11-10

The condition number of a singular matrix is infinity. The condition number of

a non-singular matrix is a measure of how close the matrix is to being

singular. The larger the value of the condition number, the closer it is to

singularity. (A singular matrix is one for which the inverse does not exist).

Try the following exercise for matrix condition number on matrix A33. The

condition number is COND(A33) , row norm, and column norm for A33 are

shown to the left. The corresponding numbers for the inverse matrix,

INV(A33), are shown to the right:

Since RNRM(A33) > CNRM(A33), then we take ||A33|| = RNRM(A33) =

21. Also, since CNRM(INV(A33)) < RNRM(INV(A33)), then we take

||INV(A33)|| = CNRM(INV(A33)) = 0.261044... Thus, the condition

number is also calculated as CNRM(A33)*CNRM(INV(A33)) = COND(A33)

= 6.7871485…

Function RANK

Function RANK determines the rank of a square matrix. Try the following

examples:

The rank of a matrix

The rank of a square matrix is the maximum number of linearly independent

rows or columns that the matrix contains. Suppose that you write a square

matrix A

as A = [c

… c

], where c

(i = 1, 2, …, n) are vectors

representing the columns of the matrix A, then, if any of those columns, say c

can be written as ,

},...,2,1{,

∑

∈≠

⋅=

njkj

jjk

d cc

1 2 ... 331 332 333 334 335 336 337 338 339 340 341 ... 863 864

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