Proof that $W^{\perp\perp}=W$ (in a finite dimensional vector space)
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
76110
Proving that the zero vector is unique
131480
Proof that composition of invertible linear transformations is invertible (without determinants)
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
156877
Rank-one perturbation proof
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
113326
Proving orthogonality of vectors in a complex vector space
114906
For $n \in \mathbb{N}$ and $W \leq \mathbb{F}^n$, there exists a homogeneous system of linear equations whose solution space is $W$
92510
Proving a vector space is infinite-dimensional
34700
Proving that the matrix exponential map is surjective onto the general linear group
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
102458
Subspace generated by permutations of a vector in a vector space
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
104578
Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
61539
proof for a basis in $L^2$