On the coefficients of the characteristic polynomial of a matrix
type: Item
instance of: scholarly article
title: On the coefficients of the characteristic polynomial of a matrix
zbMATH Open document ID: 0796.05068
DOI: 10.1016/0012-365X(94)90166-X
author: Mordechai Lewin
published in: Discrete Mathematics
publication date: 1994-09-15T00:00:00Z
review text: As is well known, the coefficients \(p_ i\) \((i=0,1, \dots, n)\) of the characteristic polynomial of a square matrix \(A\) of order \(n\) can be obtained from traces \(q_ k=\text{tr} A^ k\) \((k=0,1, \dots,n-1)\) by Newton's formulas in a recursive way. The author develops an explicit combinatorial formula yielding \(p_ i\) solely as functions of \(q_ k\). As a consequence some combinational identities as well as a statement on the characteristic polynomial of a digraph without even cycles are obtained.
reviewed by: Dragoš Cvetković
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 562669
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: square matrix
zbMATH Keywords: Newton's formulas
zbMATH Keywords: combinational identities
zbMATH Keywords: digraph
MaRDI profile type: Publication
cites work: Leverrier’s Algorithm: A New Proof and Extensions
cites work: Q3259278
cites work: Fast Parallel Matrix Inversion Algorithms
cites work: Q3907599
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full work available at URL: 0012-365x(94)90166-x
OpenAlex ID: W2474209902
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description: scientific article; zbMATH DE number 562669