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 1d comment Proving rank of $AB$ is at most equal to rank of $B$ I've looked at your answer for the past couple of days, and I still don't get it. What does $(AB)R^p) = A(B(R^p)) \subset A(R^n)$ prove? Apr23 comment Showing that linear transformations $1, T, T^2, T^3 ,\dots$ do not span the set of linear transformations of $\mathbb C^n$ into $\mathbb C^n$ like your answer. But could you just add a bit more detail for your last statement? Perhaps, an example? Apr23 accepted Showing that linear transformations $1, T, T^2, T^3 ,\dots$ do not span the set of linear transformations of $\mathbb C^n$ into $\mathbb C^n$ Apr22 comment How to use Cayley-Hamiltonian theorem in proving upper bound on linear space $W$? even if $a \neq b$? Isn't the dimension of the new I, call it $I' = a\left(\begin{array}{cc}1 & 0 \\0 & 0\end{array}\right) + b\left(\begin{array}{cc}0 & 0 \\0 & 1\end{array}\right)$. Doesn't $I'$ have dimension 2? Apr22 comment Question about projecting vector onto Subspace Just to make sure that I'm tracking: the projection listed above is the vector subspace = span($v_1,v_2$) that is closest to $v$? Apr22 revised Question about projecting vector onto Subspace fixed spelling Apr22 comment How to use Cayley-Hamiltonian theorem in proving upper bound on linear space $W$? If $I$ would have been $\left(\begin{array}{cc}a & 0 \\0 & b\end{array}\right)$, would the dimension of $W$ now be 2 (with A being the zero matrix)? Apr22 comment How to use Cayley-Hamiltonian theorem in proving upper bound on linear space $W$? @Yuval 1, correct? Apr22 comment dimension of the vector space using matrices You mean everything on the entire page answers the OP's question? Apr22 asked How to use Cayley-Hamiltonian theorem in proving upper bound on linear space $W$? Apr22 comment dimension of the vector space using matrices where on the wikipedia page should I look? Apr22 accepted Show that if $AA^t = A^tA$, then $A=A^t$ Apr22 comment Proving rank of matrix product Second question: since the rank(AB) = n-1, can we infer that the nullity of $AB$ = 1? Apr22 comment Proving rank of matrix product probably silly question, but why include the $B^{-1}$ at all? Apr22 comment Proving rank of matrix product What did you contradict? Apr22 revised Proving rank of matrix product added 49 characters in body Apr22 comment Proving rank of matrix product So $N(AB)$ = $N(A)$? Apr22 asked Proving rank of matrix product Apr22 revised Proving rank of $AB$ is at most equal to rank of $B$ added 1 character in body Apr22 accepted Find basis so matrix is in Jordan Canonical Form