Simultaneous Similarity of Matrices.

Abstract

In this paper we solve completely and explicitly the long standing problem of classifying pairs of nxn complex matrices (A,B) under a simultaneous similarity. Roughly speaking, the classification decomposes to a finite number of steps. In each step we consider an open algebraic set. Then we construct a finite number of rational functions in the entries of A and B whose values are constant on all pairs similar to (A,B). The values of the functions phi sub i (A,B), i equals 1,...,s, determine a finite number of similarity classes.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1982
Accession Number
ADA114536

Entities

People

  • Shmuel Friedland

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algebraic Functions
  • Analytic Functions
  • Classification
  • Complex Variables
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Kinetic Energy
  • Mathematics
  • New York
  • Polynomials
  • Rational Functions
  • Theorems
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Linear Algebra