Show that for every $A\in M_{n}(\mathbb{R})$ with rank(A)=1 that $||A||_{op}=||A||_{HS}$. What happens in the general case?
31302
Hilbert Schmidt Norm-Rank-inequality
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
116768
Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?
69606
How to prove rank(A+) is no more than rank(A)?
132366
Diagonalizability of $A \in M_{n}(\Bbb{R})$ (Upper traingular matrix) with all diagonal entries 1 and $A \neq I$?
66866
Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
155451
Upper bound for the rank of a nilpotent matrix , if $A^2 \ne 0$
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
102817
$A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
73773
$C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
145980
For every matrix $A\in M_{2}( \mathbb{C}) $ there's  $X\in M_{2}( \mathbb{C})$ such that $X^2=A$?
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
21758
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$