There are matrices in my course book that are called full column (row) rank matrices. I'd like to know what property of the matrix must come to mind when I see it is of full rank other than $\text{rank}(A)=\min(m,n)$ (for $A_{m\times n})$?

• being surjective if rk = #rows and injective if rk=#columns, or what do you mean? – Daniel Valenzuela Jun 20 '14 at 9:44
• One property is that you can delete rows or columns, as appropriate, to obtain a square matrix that will be invertible. – Gerry Myerson Jun 20 '14 at 9:47