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Stability of Invariant Subspaces of Quaternion Matrices

Abstract

A quaternion invariant subspace of a quaternion matrix is said to be stable (in the sense of robustness) if every nearby matrix has an invariant subspace close to the original one. Under mild hypothesis, necessary and sufficient conditions are given for quaternion invariant subspaces to be stable. Other notions of stability of quaternion invariant subspaces are studied as well, and stability criteria developed. Applications to robustness of solutions of certain classes of quaternion matrix equations are given.

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Correspondence to Leiba Rodman.

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Communicated by Daniel Aron Alpay.

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Rodman, L. Stability of Invariant Subspaces of Quaternion Matrices. Complex Anal. Oper. Theory 6, 1069–1119 (2012). https://doi.org/10.1007/s11785-012-0233-y

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Keywords

  • Quaternion matrix
  • Invariant subspace
  • Matrix equation

Mathematics Subject Classification

  • 15A24
  • 15B33
  • 15A99