Show that $V = \ker T \oplus \operatorname{im}T$ where $T$ is an idempotent linear operator
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
45130
Cyclic vector implies commuting linear operator is a polynomial
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
141286
When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
101861
How do you prove that $tr(B^{T} A )$ is a inner product?
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
145462
On the canonical isomorphism between $V$ and $V^{**}$
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
45998
The range of $T^*$ is the orthogonal complement of $\ker(T)$
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
55388
Finding nilpotent and diagonalizable operators for a linear transformation $T$
24072
Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$
83970
Proof of an elementary property of Projection Operators
117131
Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
144104
Show that a positive operator on a complex Hilbert space is self-adjoint
99942
A normal, idempotent linear operator must be self-adjoint
86084
Why is $T$ normal and idempotent?