Results 11 to 20 of about 2,503,474 (234)

The poset of the nilpotent commutator of a nilpotent matrix [PDF]

Linear Algebra and its Applications, 2012
Let $B$ be an $n \times n$ nilpotent matrix with entries in an infinite field $\k$. Assume that $B$ is in Jordan canonical form with the associated Jordan block partition $P$.
Leila Khatami
semanticscholar   +5 more sources

The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix [PDF]

Linear and Multilinear Algebra, 2007
We study the set ( ) of all possible Jordan canonical forms of nilpotent matrices commuting with a given nilpotent matrix B. We describe ( ) in the special case when B has only one Jordan block and discuss some consequences.
Polona Oblak
semanticscholar   +5 more sources

On the nilpotent commutator of a nilpotent matrix [PDF]

Linear and Multilinear Algebra, 2011
We study the structure of the nilpotent commutator 𝒩 B of a nilpotent matrix B. We show that 𝒩 B intersects all nilpotent orbits for conjugation if and only if B is a square-zero matrix.
Polona Oblak
semanticscholar   +6 more sources

Algorithms for computing with nilpotent matrix groups over infinite domains [PDF]

Journal of Symbolic Computation, 2019
We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups.
A. Detinko, D. Flannery
semanticscholar   +7 more sources

Bound on the Jordan type of a generic nilpotent matrix commuting with a given matrix [PDF]

Journal of Algebraic Combinatorics, 2012
It is well known that a nilpotent n×n matrix B is determined up to conjugacy by a partition of n formed by the sizes of the Jordan blocks of B. We call this partition the Jordan type of B.
A. Iarrobino, Leila Khatami
semanticscholar   +6 more sources

Nilpotents Leave No Trace: A Matrix Mystery for Pandemic Times

Journal of Humanistic Mathematics, 2022
Reopening a cold case, inspector Echelon, high-ranking in the Row Operations Center, is searching for a lost linear map, known to be nilpotent. When a partially decomposed matrix is unearthed, he reconstructs its reduced form, finding it singular. But were its roots nilpotent?
Eric L. Grinberg
openaire   +4 more sources

$L^p$ Matrix Coefficients for Nilpotent Lie Groups [PDF]

Rocky Mountain Journal of Mathematics, 1996
Suppose that \(G\) is a connected nilpotent Lie group. For any irreducible unitary representation \(\pi\) of \(G\), denote by \(N_\pi\) its kernel. The main theorem of the paper under review is that there exists \(p\) in \([2,\infty)\), depending only on \(G\), such that the matrix coefficients \(g\mapsto\langle\pi(g)\xi,\eta\rangle\) lie in \(L^p(G/N_\
Corwin, Lawrence, Moore, Calvin C.
openaire   +4 more sources

Sign pattern matrices that allow a nilpotent matrix [PDF]

Bulletin of the Australian Mathematical Society, 1996
We characterise some star sign pattern matrices and linear tree sign pattern matrices that allow a nilpotent matrix.
Lina Yeh
semanticscholar   +3 more sources

A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field [PDF]

The Scientific World Journal, 2013
Let be an arbitrary field and a square matrix over . Then is sum of two square nilpotent matrices over if and only if, for every algebraic extension of and arbitrary nonzero , there exist idempotent matrices and over such that .
Xiaofei Song, Baodong Zheng, Chongguang Cao   +2 more
doaj   +2 more sources

On the distance from a matrix to nilpotents [PDF]

Linear Algebra and its Applications, 2023
We prove that the distance from an $n\times n$ complex matrix $M$ to the set of nilpotents is at least $\frac{1}{2}\sec\fracπ{n+2}$ if there is a nonzero projection $P$ such that $PMP=M$ and $M^*M\geq P$. In the particular case where $M$ equals $P$, this verifies a conjecture by G.W. MacDonald in 1995.
Michiya Mori
openaire   +3 more sources