What is the rank of a matrix?

1 Answer
Jul 24, 2018

Answer:

Please see the explanation below

Explanation:

Let #A# be a #(m xxn)# matrix.

Then #A# consists of #n # column vectors #(a_1, a_2,...a_n)# which are #m# vectors.

The rank of #A# is the maximum number of linearly independent column vectors in #A#, that is, the maximun number of independent vectors among #(a_1,a_2, ...a_n)#

If #A=0#, the rank of #A# is #=0#

We write #rk(A)# for the rank of #A#

To find the rank of a matrix #A#, use Gauss elimination.

The rank of the transpose of #A# is the same as the rank of #A#.

#rk(A^T)=rk(A)#