$V$ be a f.d, vector space over complex field , $P_1,...,P_n$ projection linear operators such that $P_1+...+P_n=I$ , then $P_iP_j=O,\forall i\ne j$?
111191
Show that $P_i$ and $\sum_i P_i$ being idempotent implies $P_i P_j=\delta_{ij}$
133711
Orthogonal basis for infinite-dimensional vector spaces
114510
Inner Product Spaces
137890
Diagonalizable Operators and characteristic polynomials
112205
Which of the following polynomials are subspaces of $\mathbb{P}_n$ for an appropriate value of n?
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
56102
Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
43503
Bases of complex vector spaces and the axiom of choice
99942
A normal, idempotent linear operator must be self-adjoint
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
18373
Can infinite-dimensional vector spaces be decomposed into direct sum of its subspaces?
72077
''Linear'' transformations between vector spaces over different fields .
67106
Projection on the hyperplane $H: \sum x_i=0$
144019
A strictly positive operator is invertible
49759
Proving that $i\hbar\frac{\partial}{\partial \mathbf{p}}$ is the operator of $\mathbf{x}$ in momentum space
144048
Linear Operators satisfying $S^n=0$ but $S^{n-1}\neq 0$
68526
Polynomials as vector spaces?