Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V..
119782
Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.
4319
Vector space can be written as direct sum of subspaces
17087
Question concerning linear combinations of vectors and linear independence in Linear Algebra.
137873
Problems that involves two facts in the definition of vector spaces
79457
Geometric random variables $X_1:G(p_1)$ $X_2:G(p_2)$ $X_3:G(p_3)$ are independent, prove the following :
40409
If a subspace S is spanned by $n$ vectors, any subset of S with $m>n$ vectors is linearly dependent
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
76160
Dimension of the sum of two vector subspaces
92600
Let $V$ be a $K$-vector space, $f: V \rightarrow V$ a linear map. Under some condition, show that $v, f(v),...,f^n(v)$ are linearly independent.
43504
Proving the existence of a complement subspace $U' \subset V$.
140711
Linear independence of images by $A$ of vectors whose span trivially intersects $\ker(A)$
59803
Converse of Schur's Lemma in finite dimensional vector spaces
97801
If $R_{1}$ and $R_{2}$ are relations on a set S with $R_{1};R_{2}=R_{2};R_{1}$. Then $R_{1}$ and $R_{2}$ are bijective maps
133087
Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
88728
Dimensions of vector subspaces in a direct sum are additive
30017
Orthogonality and linear independence
113326
Proving orthogonality of vectors in a complex vector space