query: If $A^m = 0$, then $\mbox{rank}(A) \leq \frac{m-1}{m}{n}$
positive_passages.docid: 155451
positive_passages.text: Upper bound for the rank of a nilpotent matrix , if $A^2 \ne 0$
negative_passages.docid: 118244
negative_passages.text: An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
negative_passages.docid: 97040
negative_passages.text: Question about an application of the Rank-Nullity theorem
negative_passages.docid: 138632
negative_passages.text: Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
negative_passages.docid: 64747
negative_passages.text: If $A^m=I$ then A is Diagonalizable
negative_passages.docid: 65062
negative_passages.text: Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
negative_passages.docid: 18477
negative_passages.text: $(W_1+W_2+\cdots+W_n)^a \leq W_1^a +\cdots + W_n^a$ for $n$ integer, $n\geq 2$, $W\gt 0$ and $a$ constant, real, $0\lt a\lt 1$
negative_passages.docid: 97487
negative_passages.text: How to prove whether a matrix has rank $1$
negative_passages.docid: 65162
negative_passages.text: 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.
negative_passages.docid: 25981
negative_passages.text: Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
negative_passages.docid: 27821
negative_passages.text: A problem on rank of $A$ and $\operatorname{adj}(A)$
negative_passages.docid: 10483
negative_passages.text: Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$
negative_passages.docid: 137148
negative_passages.text: If $A=\left( \begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{array} \right)$, find the rank of $A+A^2+A^3$
negative_passages.docid: 83049
negative_passages.text: Frobenius Inequality Rank
negative_passages.docid: 20922
negative_passages.text: If all minors are $0$, the rank is at most $n-2$
negative_passages.docid: 80826
negative_passages.text: To prove $\left|\frac{p_n(z)}{q_m(z)}\right|\leq \frac{M}{|z|^{m-n}}$ for some $M>0$
negative_passages.docid: 90962
negative_passages.text: For positive integers $m,n$ if $\sqrt 7 - \frac{m}{n} > 0$ then prove that $\sqrt 7 - \frac{m}{n} > \frac{1}{{mn}}$