Multiplication of two projection operators is zero if they sum to the identity
69474
Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow  P_{j}P_{i}=0$
88728
Dimensions of vector subspaces in a direct sum are additive
1162
Why $\{\mathbf{0}\}$ has dimension zero?
128875
Expectation values of the position operator is equal to zero in case of even potentials?
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
35625
Direct sum of orthogonal subspaces
25039
Zero vector of a vector space
102816
multiplication equivalent of the summation symbol
52621
Why is $\det(A - \lambda I)$ zero?
118996
Prove that $T$ is an orthogonal projection
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
119684
Is a contraction idempotent operator self-adjoint?
76160
Dimension of the sum of two vector subspaces
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
127025
Diagonalization of a projection
144048
Linear Operators satisfying $S^n=0$ but $S^{n-1}\neq 0$
65888
A counterexample to theorem about orthogonal projection