HP (Hewlett-Packard) 50g ユーザーズマニュアル

Page 11-11

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 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

n

×n

 as A = [c

1

2

 … c

n

], where c

i

 (i = 1, 2, …, n) are vectors 

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

k

,

can be written as 

,

}

,...,

2

,

1

{

,

∑

∈

≠

⋅

=

n

j

k

j

j

j

k

d

c

c