query: A nilpotent matrix is similar to a strictly upper triangular matrix
positive_passages.docid: 144531
positive_passages.text: How to prove that a nilpotent operator has a basis representation that is strictly upper triangular?
negative_passages.docid: 121100
negative_passages.text: Rootspaces are $\mathop{ad}$ nilpotent
negative_passages.docid: 11566
negative_passages.text: Similar matrices and minimal polynomial
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: 130004
negative_passages.text: Jacobson radical equal to nilradical in $R[X]$
negative_passages.docid: 113907
negative_passages.text: All nilpotent $2\times 2$ matrices
negative_passages.docid: 19132
negative_passages.text: Similar matrices have the same eigenvalues with the same geometric multiplicity
negative_passages.docid: 115905
negative_passages.text: The determinant of block triangular matrix as product of determinants of diagonal blocks
negative_passages.docid: 32767
negative_passages.text: Similar Matrices and Linear Transformations
negative_passages.docid: 31116
negative_passages.text: Matrix given by $a_{ij} = 1/(i+j)$ is non-singular.
negative_passages.docid: 98541
negative_passages.text: If a Matrix Has Only Zero as an Eigen-Value Then It Is Nilpotent
negative_passages.docid: 106322
negative_passages.text: Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.
negative_passages.docid: 18036
negative_passages.text: Localization by a non-nilpotent as a polynomial quotient
negative_passages.docid: 30889
negative_passages.text: Classifying complex $2\times 2$ matrices up to similarity
negative_passages.docid: 130268
negative_passages.text: How to prove that a nilpotent matrix is not invertible?
negative_passages.docid: 131972
negative_passages.text: All nilpotent $2 \times 2$ matrices satisfy $A^{2}=0$
negative_passages.docid: 146046
negative_passages.text: Are two matrices having the same characteristic and minimal polynomial always similar?