How to show a matrix is full rank? I have some discussion with my friend about matrix rank.
But we find that even we know how to compute rank, we don't know how to show the matrix is full rank.
How to show this?

If you are talking about square matrices, just compute the determinant.
If that is non-zero, the matrix is of full rank.
If the matrix $A$ is $n$ by $m$, assume wlog that $m\leq n$ and compute all determinants of $m$ by $m$ submatrices.  If one of them is non-zero, the matrix has full rank.
Also, you can solve the linear equation $Ax=0$ and figure out what dimension the space of solutions has.  If the dimension of that space is $n-m$, then the matrix is of full rank.
Note that a matrix has the same rank as its transpose.
