query: If $V$ is finite-dimensional with $J : V \to V$ such that $J^2 = -id$, then $V$ has even dimension
positive_passages.docid: 20879
positive_passages.text: Let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. How can we show that $n$ is even?
negative_passages.docid: 38033
negative_passages.text: A surjective linear map into a finite dimensional space is open
negative_passages.docid: 7457
negative_passages.text: Prove that $J^+AJ$ has positive eigenvalues
negative_passages.docid: 74024
negative_passages.text: Higher dimensional equivalent of complex numbers
negative_passages.docid: 158308
negative_passages.text: Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
negative_passages.docid: 59803
negative_passages.text: Converse of Schur's Lemma in finite dimensional vector spaces
negative_passages.docid: 92510
negative_passages.text: Proving a vector space is infinite-dimensional
negative_passages.docid: 13899
negative_passages.text: Proof that $-v = (-1)*v$
negative_passages.docid: 152104
negative_passages.text: How do I prove that $ij = k?$
negative_passages.docid: 142097
negative_passages.text: Finding the dimension of the orthogonal complement
negative_passages.docid: 26398
negative_passages.text: Group of even order contains an element of order 2
negative_passages.docid: 125966
negative_passages.text: Why there's a finite $\Gamma '$ such that $\Gamma ' \vDash \varphi$?
negative_passages.docid: 82578
negative_passages.text: Show that if $G$ is $2-$connected, then for any two vertices $u$ and $v$ there exists a cycle $C$ such that $u, v \in V (C)$
negative_passages.docid: 95513
negative_passages.text: Proving $W$ is a subspace of $P_{2}$
negative_passages.docid: 143095
negative_passages.text: If an $H\le G$ has an irreducible representation of dimension $d$, then show $G$ has an irreducible representation of at least dimension $d$.
negative_passages.docid: 126060
negative_passages.text: Proving that a Euler Circuit has a even degree for every vertex
negative_passages.docid: 13914
negative_passages.text: If $a^2+b^2=c^2$ then $a$ or $b$ is even.