Corpus ID: 232478579

Infimum of a matrix norm of A induced by an absolute vector norm

  title={Infimum of a matrix norm of A induced by an absolute vector norm},
  author={Shmuel Friedland},
We characterize the infimum of a matrix norm of a square matrix A induced by an absolute norm, over the fields of real and complex numbers. Usually this infimum is greater than the spectral radius of A. If A is sign equivalent to a nonnegative matrix B then this infimum is the spectral radius of B. 2020 Mathematics Subject Classification. 15A42, 15A60, 15B48. 


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Matrices-algebra, analysis and applications, World Scientific Publishing Co
  • Pte. Ltd., Hackensack, NJ,
  • 2016
Matrix analysis, Second edition
  • 2013