If $W_j$ is the subspace associated to $\lambda_j$ for $j\in{1,...,k}$ prove that $W_1,...,W_k$ are independent
109675
Finite sum of eigenspaces (with distinct eigenvalues) is a direct sum
156727
A step in the proof of Characterization of $W^{1,\infty}$
67191
When is the union of a family of subspaces of a vector space also a subspace?
132487
Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$
19946
Let $W$ be a given subspace of $V$ find the orthogonal complement $W^{\perp}$
70475
Proving a basis for inner product space V when $||e_j-v_j||< \frac{1}{\sqrt{n}}$.
22295
Subspace of a separable space is separable
96354
Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
6547
Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
155228
$X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
24585
Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
91087
For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent?
34712
Decomposable elements of $\Lambda^k(V)$
107248
Prove that the set $ \{\sin(x),\cos(x),\sin(2x),\cos(2x)\}$ is linearly independent.
126769
Linear independence of columns implies non-zero determinant
58329
Show that $y_1$ and $y_2$ are not Linearly Independent
62058
How to prove $1$,$\sqrt{2},\sqrt{3}$ and $\sqrt{6}$ are linearly independent over $\mathbb{Q}$?