Let K=A^T C A, where C0. Prove that (a) ker K=coker K=ker A; (b) img K=coimg K=coimg A.

Question

Let K=A^T C A, where C>0. Prove that (a) ker K=coker K=ker A; (b) img K=coimg K=coimg A.

Accepted Answer

Step 1:u000AFirst, letu0027s understand the notation and what we need to prove. $A$ is a matrix, $C$ is

Let $K=A^T C A$, where $C>0$. Prove that (a) $\operatorname{ker} K=\operatorname{coker} K=\operatorname{ker} A$; (b) $\operatorname{img} K=\operatorname{coimg} K=\operatorname{coimg} A$.