Prove that $T=T^2$ if and only if $T$ is a projection on $W_1=\{y\in V:T(y)=y\}$ along $N(T)$
54217
Let $V$ be a vector space. Determine all linear transformations $T:V \rightarrow V$ such that $T=T^2$.
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
145600
Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?
92033
Prove that $g$ is a submanifold: $g (t,u,v) = (t^2,u^2,v^2,\sqrt{2}uv, \sqrt{2}tv,\sqrt{2}tu)$
15596
Identification of each tangent space $T_pV$ with $V$ itself?
149907
$T\circ T=0:V\rightarrow V \implies R(T) \subset N(T)$
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
101467
Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.
90345
If $\lVert x\rVert=\lVert y \rVert$, prove that exists a unitary transformation such as $Tx=y$
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
144097
eigenvalues and eigenvectors of $vv^T$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
149801
prove that $TS = ST$
95379
Prove that $V = V_1 \oplus V_2$ in the following
63465
Orthogonal Projection of $ z $ onto the Affine set $ \left\{ x \mid A x = b \right\} $
143608
Show the Trace$(B)^{2} \leq$ nTrace$(B^{T}B)$