query: Let $V$ be a finite-dimensional vector space over $F$, Suppose that $E_1,...,E_k$ are projections of $V$
positive_passages.docid: 111191
positive_passages.text: Show that $P_i$ and $\sum_i P_i$ being idempotent implies $P_i P_j=\delta_{ij}$
negative_passages.docid: 93165
negative_passages.text: A projection satisfying $\| Px \| \leq \|x\|$ for all $x$ is an orthogonal projection
negative_passages.docid: 92600
negative_passages.text: 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.
negative_passages.docid: 92510
negative_passages.text: Proving a vector space is infinite-dimensional
negative_passages.docid: 132300
negative_passages.text: Dimensions of vector spaces in an exact sequence
negative_passages.docid: 134065
negative_passages.text: A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
negative_passages.docid: 154762
negative_passages.text: Dual space of a finite dimensional normed space
negative_passages.docid: 4151
negative_passages.text: Every subspace of a vector space has a complement
negative_passages.docid: 9854
negative_passages.text: If $U$ is a neighborhood of $e$, there exists $V$ neighborhood of $e$ such that $V^{-1}V \subseteq U$
negative_passages.docid: 60685
negative_passages.text: The vector space formed on C[0,1] and the norm $(\int_{0}^{1}|f(t)|^2 dt)^{1/2} $
negative_passages.docid: 94405
negative_passages.text: Let $W$ be the set of all linear combinations of $v_1,...,v_n$. Then $W$ is a subspace of $V$.
negative_passages.docid: 137873
negative_passages.text: Problems that involves two facts in the definition of vector spaces
negative_passages.docid: 112024
negative_passages.text: Let $T:V → V$ be a linear transformation where $V$ is finite dimensional.
negative_passages.docid: 124786
negative_passages.text: Prove that V contains a subspace of each dimension
negative_passages.docid: 51397
negative_passages.text: 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 $V$
negative_passages.docid: 47015
negative_passages.text: Vector Space Structures over ($\mathbb{R}$,+)
negative_passages.docid: 146143
negative_passages.text: Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands