If $V$ over $\mathbb{C}$, $\dim V\ge 2$, let $q: V \rightarrow \Bbb{C}$ be a Quadratic form. s.t. exists $v \ne 0$ such that $q(v)=0$
34206
Quadratic form under $\mathbb{C}$ finite-dimension vector space always have a nonzero vector that yields zero?
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
114575
If $\sum_{i=1}^k \dim F_i > n(k-1)$ then $\cap_{i=1}^k F_i \neq \{0\}$
125763
If $\mathrm{tr}(A)=0$, then we have $A=BC-CB?$
125702
There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
95669
Solutions of $|z| = z^5$ in $\Bbb{C}$?
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
3433
Proof if $a \vec v = 0$ then $a = 0$ or $\vec v = 0$
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
115004
If $x\notin\mathbb Q$, then $\left|x-\frac{p}{q}\right|<\frac{1}{q^2}$ for infinitely many $\frac{p}{q}$?
152451
REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
105141
$\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
111550
Let $A$ be a square complex matrix of size $n$ then $\langle Ax,x\rangle=0$ for $\forall x \in \Bbb C^n$ $\iff A=0$
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
150674
Uniqueness in existence of a bilinear form