Prove that if the norms of vectors are equal, there is a unitary transformation such that $Tx=y$
90345
If $\lVert x\rVert=\lVert y \rVert$, prove that exists a unitary transformation such as $Tx=y$
48238
Prove the positive definiteness of Hilbert matrix
36771
How to prove that A is normal if and only if there's a unitary matrix V,s.t. A*=AV?
144382
Proving $\lVert x \rVert_3$ is smaller than euclidean norm
94844
Unitary map between sets of vectors
151161
norms on vector space are equivalent iff they have same topology
18921
Linear Transformations: Proving 1 dimensional subspace goes to 1 dimensional
118996
Prove that $T$ is an orthogonal projection
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
81879
$Av=λv$ basis proof problems
158845
Given $A$ and $B$ positive-definite matrices and $Q$ unitary matrix, prove that if $A = BQ$, then $A=B$.
62425
Equivalent Definitions of the Operator Norm
59055
Diagonalizable transformation restricted to an invariant subspace is diagonalizable
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
62887
Proof that a linear transformation is continuous
131480
Proof that composition of invertible linear transformations is invertible (without determinants)