# Function Rank - HP F2226A - 48GII Graphic Calculator User Manual

Graphing calculator.

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
×
n
n
1
representing the columns of the matrix A, then, if any of those columns, say c
c
can be written as
k
... c
], where c
(i = 1, 2, ..., n) are vectors
2
n
i
d c
,
j
j
j
k
, ∈
j
1 {
2 ,
,...,
n
}
,
k
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