query: How to prove $A^n = 0$ if $A$ is an $n\times n$ strictly upper triangular matrix
positive_passages.docid: 50404
positive_passages.text: How to prove a matrix is nilpotent?
negative_passages.docid: 96152
negative_passages.text: Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
negative_passages.docid: 78224
negative_passages.text: Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
negative_passages.docid: 22666
negative_passages.text: Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
negative_passages.docid: 82295
negative_passages.text: Showing that the minimal polynomial of an $n \times n$ matrix has degree at most $n$ without using the Cayley-Hamilton Theorem
negative_passages.docid: 89279
negative_passages.text: If $\sum a_n/k^n = 0$ for all $k$, then $a_n = 0$ for all $n$
negative_passages.docid: 57981
negative_passages.text: Alternative proof of $a\times0= 0$
negative_passages.docid: 10478
negative_passages.text: Matrix reciprocal positive to prove $λ_{max⁡}=n$
negative_passages.docid: 118471
negative_passages.text: Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
negative_passages.docid: 133758
negative_passages.text: Traces of powers of a matrix $A$ over an algebra are zero implies $A$ nilpotent.
negative_passages.docid: 61274
negative_passages.text: If $AA^T$ is the zero matrix, then $A$ is the zero matrix
negative_passages.docid: 38635
negative_passages.text: How to prove that the matrix $A^k$ approaches $0$ as $k$ approaches infinity
negative_passages.docid: 121982
negative_passages.text: Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
negative_passages.docid: 111550
negative_passages.text: Let $A$ be a square complex matrix of size $n$ then $\langle Ax,x\rangle=0$ for $\forall x \in \Bbb C^n$ $\iff A=0$
negative_passages.docid: 71451
negative_passages.text: A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$
negative_passages.docid: 124942
negative_passages.text: Prove that an upper triangular matrix is invertible if and only if every diagonal entry is non-zero.
negative_passages.docid: 118283
negative_passages.text: Show that if $A^{n}=I$ then $A$ is diagonalizable.