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Partitioned Matrices, Rank, and Eigenvalues

  • Fuzhen ZhangEmail author
Chapter
  • 7.7k Downloads
Part of the Universitext book series (UTX)

Abstract

We begin with the elementary operations on partitioned (block) matrices, followed by discussions of the inverse and rank of the sum and product of matrices. We then present four different proofs of the theorem that the products AB and BA of matrices A and B of sizes m × n and n × m, respectively, have the same nonzero eigenvalues. At the end of this chapter we discuss the often-used matrix technique of continuity argument and the tool for localizing eigenvalues by means of the Ger?sgorin discs.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Division of Math, Science, and TechnologyNova Southeastern UniversityFort LauderdaleUSA

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