If A is matrix m by n and B is matrix n by r
The rank of matrix AB ought to be minimum of rank(A) or rank(B) how may i prove this? Thanks
If A is matrix m by n and B is matrix n by r
The rank of matrix AB ought to be minimum of rank(A) or rank(B) how may i prove this? Thanks
No. The product of two rank $1$ matrices may have rank $0$. $\begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix} \begin{bmatrix} 0 & 0 \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$