If U is a T-invariant subspace of V is there necessarily another T-invariant subspace$-W S.T. U\oplus W = V?$
59531
Do $T$-invariant subspaces necessarily have a $T$-invariant complement?
51397
If a field $F$ is such that $\left|F\right|>n-1$ why is $V$ a vector space over $F$ not equal to the union of $n$ proper subspaces of $V$
15560
Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
114309
T-invariant linear independence
90525
The subspace of $\ell_2$
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
41013
Subspace of $C^3$ that spanned by a set over C and over R
125785
Minimal polynomial of restriction to invariant subspace divides minimal polynomial
94405
Let $W$ be the set of all linear combinations of $v_1,...,v_n$. Then $W$ is a subspace of $V$.
88728
Dimensions of vector subspaces in a direct sum are additive
141794
Invariant subspaces of specific dimension
18373
Can infinite-dimensional vector spaces be decomposed into direct sum of its subspaces?
119671
Is there an infinite dimensional $V$ such that every linear operator on $V$ is a direct sum of a nilpotent and  an invertible operator?
90757
$T$ self-adjoint on Hilbert space $H$, $T^n=T^{n+1}$ will $T$ be an orthogonal projection operator?
82464
$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces