Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
35013
Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
95379
Prove that $V = V_1 \oplus V_2$ in the following
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Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
113326
Proving orthogonality of vectors in a complex vector space
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
4240
The proof of Triple Vector Products
41013
Subspace of $C^3$ that spanned by a set over C and over R
118996
Prove that $T$ is an orthogonal projection
1799
How many k-dimensional subspaces there are in n-dimensional vector space over $\mathbb F_p$?
16512
Product of $T_1$ spaces is $T_1$
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Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?
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Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
100107
How can I prove that a linear map $T:V\to V$ such that $T^2 = I$ is equal to the Identity map?
41347
The dimension of the intersection of two vector subspaces
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
20879
Let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. How can we show that $n$ is even?
15560
Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.