Prove that if $T,U: V \rightarrow V$ are linear operators on an inner product space, then $(TU)^* = U^*T^*$
46669
How can I prove these are the adjoint operators?
144097
eigenvalues and eigenvectors of $vv^T$
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
44685
Inner product on $C(\mathbb R)$
22297
Normal operator $\Rightarrow$ S invariant implies $S^\perp$ invariant
100107
How can I prove that a linear map $T:V\to V$ such that $T^2 = I$ is equal to the Identity map?
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
70475
Proving a basis for inner product space V when $||e_j-v_j||< \frac{1}{\sqrt{n}}$.
95379
Prove that $V = V_1 \oplus V_2$ in the following
32606
Is the operator $T((x_1,x_2,...,x_n))=(x_1,\frac{x_2}2,\frac{x_3}3,...)$ on $\ell^2$ self-adjoint and unitary
140835
Inner Product Space Inequality
69893
An inner product space and its proper closed subspace with trivial orthogonal complement
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
89089
Prove that there is a unique inner product on $V$
77891
$(U\circ T)^{*} = T^{*}\circ U^{*}$
54217
Let $V$ be a vector space. Determine all linear transformations $T:V \rightarrow V$ such that $T=T^2$.