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Jun
18
awarded  Famous Question
Jun
13
awarded  Popular Question
Jun
7
comment What is the dimension of the space $V$ of all matrices $S$
I really wished you had worked more of the problem out. I'm having a hard time following the reasoning.
Apr
27
comment Determine rank and nullity of linear transformation between polynomial of degree $\leq$ 5 to $R^6$
got it. but what about the second part?
Apr
27
comment Determine rank and nullity of linear transformation between polynomial of degree $\leq$ 5 to $R^6$
I'm not sure what should follow the "so..."
Apr
27
asked Determine rank and nullity of linear transformation between polynomial of degree $\leq$ 5 to $R^6$
Apr
27
asked Trouble finding Jordan Normal form for $4 \times $ 4 matrix
Apr
25
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?