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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?
Apr
23
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?
Apr
23
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$
Apr
22
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?
Apr
22
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 $v$?
Apr
22
revised Question about projecting vector onto Subspace
fixed spelling
Apr
22
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)?
Apr
22
comment How to use Cayley-Hamiltonian theorem in proving upper bound on linear space $W$?
@Yuval 1, correct?
Apr
22
comment dimension of the vector space using matrices
You mean everything on the entire page answers the OP's question?
Apr
22
asked How to use Cayley-Hamiltonian theorem in proving upper bound on linear space $W$?
Apr
22
comment dimension of the vector space using matrices
where on the wikipedia page should I look?
Apr
22
accepted Show that if $AA^t = A^tA$, then $A=A^t$
Apr
22
comment Proving rank of matrix product
Second question: since the rank(AB) = n-1, can we infer that the nullity of $AB$ = 1?
Apr
22
comment Proving rank of matrix product
probably silly question, but why include the $B^{-1}$ at all?
Apr
22
comment Proving rank of matrix product
What did you contradict?
Apr
22
revised Proving rank of matrix product
added 49 characters in body
Apr
22
comment Proving rank of matrix product
So $N(AB)$ = $N(A)$?
Apr
22
asked Proving rank of matrix product
Apr
22
revised Proving rank of $AB$ is at most equal to rank of $B$
added 1 character in body
Apr
22
accepted Find basis so matrix is in Jordan Canonical Form