query: Let V= Mat2×2(K) be a 4-dimensional vector space with the basis
positive_passages.docid: 17421
positive_passages.text: Linear Algebra: Find a matrix A such that T(x) is Ax for each x
negative_passages.docid: 123505
negative_passages.text: how to prove vector norm equivalence in finite dimensional space($\mathbb{R}^{n}$)?
negative_passages.docid: 18913
negative_passages.text: How to find a basis for the intersection of two vector spaces in $\mathbb{R}^n$?
negative_passages.docid: 148101
negative_passages.text: Basis for $\mathbb{Z}^2$
negative_passages.docid: 4319
negative_passages.text: Vector space can be written as direct sum of subspaces
negative_passages.docid: 154724
negative_passages.text: Every vector space has a basis
negative_passages.docid: 119782
negative_passages.text: 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.
negative_passages.docid: 95379
negative_passages.text: Prove that $V = V_1 \oplus V_2$ in the following
negative_passages.docid: 79061
negative_passages.text: show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
negative_passages.docid: 38378
negative_passages.text: $M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
negative_passages.docid: 41347
negative_passages.text: The dimension of the intersection of two vector subspaces
negative_passages.docid: 62303
negative_passages.text: For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
negative_passages.docid: 37794
negative_passages.text: Proving the two given vectors are orthogonal
negative_passages.docid: 88728
negative_passages.text: Dimensions of vector subspaces in a direct sum are additive
negative_passages.docid: 92291
negative_passages.text: $U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
negative_passages.docid: 106408
negative_passages.text: Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
negative_passages.docid: 89517
negative_passages.text: Do four dimensional vectors have a cross product property?