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The tan \(\theta \) theorem with relaxed conditions

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Publication:665971
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DOI10.1016/j.laa.2011.08.038zbMath1244.15013OpenAlexW2021244397MaRDI QIDQ665971

Yuji Nakatsukasa

Publication date: 7 March 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2011.08.038


zbMATH Keywords

eigenvectorHermitian matrixcanonical anglesgeneralized tan\(\theta\) theorem


Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42)


Related Items

Alternative proof of the a priori \(\tan \theta\) theorem ⋮ The tan Θ theorem for definite matrix pairs ⋮ Rayleigh--Ritz Majorization Error Bounds of Mixed Type ⋮ Majorization Bounds for Ritz Values of Self-Adjoint Matrices


Uses Software

  • JDQR
  • JDQZ
  • lobpcg.m


Cites Work

  • Unnamed Item
  • History and generality of the CS decomposition
  • Matrix Algorithms
  • Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
  • Matrix Analysis
  • On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
  • Templates for the Solution of Algebraic Eigenvalue Problems
  • The Rotation of Eigenvectors by a Perturbation. III
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