# Function Rank - HP 50g User Manual

Graphing calculator.

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