query: $-(-v) = v$ for any $v \in V$
positive_passages.docid: 146339
positive_passages.text: Proof of -(-v)=v in a vector space
negative_passages.docid: 131998
negative_passages.text: let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
negative_passages.docid: 35564
negative_passages.text: Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$
negative_passages.docid: 107397
negative_passages.text: Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
negative_passages.docid: 111763
negative_passages.text: True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
negative_passages.docid: 51465
negative_passages.text: New, elegant proofs for $\varphi(p^{k})=p^{k}-p^{k-1}$
negative_passages.docid: 68449
negative_passages.text: $\operatorname{Supp}(M)=V(\operatorname{Ann}M)$ if $M$ is finitely generated
negative_passages.docid: 82597
negative_passages.text: How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
negative_passages.docid: 109674
negative_passages.text: If $(I-T)^{-1}$ exists, can it always be written in a series representation?
negative_passages.docid: 4240
negative_passages.text: The proof of Triple Vector Products
negative_passages.docid: 41044
negative_passages.text: Equivalence of $a \rightarrow b$ and $\lnot a \vee b$
negative_passages.docid: 33542
negative_passages.text: When is $A- B = B- A$?
negative_passages.docid: 111515
negative_passages.text: Proving that $-a=(-1)\cdot a$
negative_passages.docid: 101320
negative_passages.text: How to tell $i$ from $-i$?
negative_passages.docid: 57649
negative_passages.text: Prove that for every $f$, a bilinear form, there exists a basis ${v_1,...,v_n}$ so that $f(v_i,v_j) = -f(v_j,v_i)$
negative_passages.docid: 40070
negative_passages.text: Is there a real-valued function $f$ such that $f(f(x)) = -x$?
negative_passages.docid: 105367
negative_passages.text: Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$