query: Prove that for each $n$-dimensional column vector $\xi$, the equation $A'(A^2+A)X=A'\xi$ has a nonzero solution.
positive_passages.docid: 18914
positive_passages.text: How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
negative_passages.docid: 119407
negative_passages.text: Solution of Vector equation
negative_passages.docid: 89089
negative_passages.text: Prove that there is a unique inner product on $V$
negative_passages.docid: 117352
negative_passages.text: Show $x^n+ax+b=0$ has most two solutions
negative_passages.docid: 56818
negative_passages.text: Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
negative_passages.docid: 57771
negative_passages.text: Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
negative_passages.docid: 42713
negative_passages.text: Solutions to the equation $ze^{a-z}=1$
negative_passages.docid: 61539
negative_passages.text: proof for a basis in $L^2$
negative_passages.docid: 154327
negative_passages.text: $A^2X = X$ show that $AX = X$, if $A_{ij} > 0$ and $x_{i} > 0$
negative_passages.docid: 142538
negative_passages.text: The number of solutions to an $n^{th}$ order differential equation.
negative_passages.docid: 65000
negative_passages.text: prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
negative_passages.docid: 55377
negative_passages.text: Non-zero eigenvalues of $AA^T$ and $A^TA$
negative_passages.docid: 100845
negative_passages.text: How to prove that $G(x)=ax+b$ is a one-to-one correspondence where $a\neq0$ and $a,b\in\mathbb{R}$.
negative_passages.docid: 46106
negative_passages.text: Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
negative_passages.docid: 54628
negative_passages.text: Properties of non-zero symmetric bilinear form
negative_passages.docid: 34206
negative_passages.text: Quadratic form under $\mathbb{C}$ finite-dimension vector space always have a nonzero vector that yields zero?
negative_passages.docid: 89705
negative_passages.text: How to solve $a_n = 2a_{n-1} + 1, a_0 = 0, a_1 = 1$?