Let A be an m times n matrix with rank r 1 With your group i

Let A be an m times n matrix with rank r. 1. With your group, investigate the relationship between m, n and r. What can you conclude about how r relates to m and n?

Solution

Let A be an m x n matrix with rank r .

The rank of any matrix is the number of linearly independent rows, which is the same as the number of linearly independent columns.

The maximum this value can be is therefore the maximum of the minimum of the dimensions of the matrix,

or rank ( A ) min ( m, n )

.