2
$\begingroup$

Let $A\in\text{Mat}_{m,n}(K)$ be an $m\times n$ matrix with coefficients in a field $K$. Then the kernel is often defined in set-builder notation as $\ker(A)=\{x\in K^n|Ax=0 \}$. I would like to know if, like the image of $A$, the kernel can be expressed explicitly in terms of the entries for a general matrix $A=(A)_{ij}$? This seems unlikely as we need to know the zero columns of $A$ after a Gaussian elimination. But, perhaps there is another definition.

Thanks in advance!

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.