Question

What is the rank of a matrix?

Answer 1

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)`