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Journal of Mathematical Sciences

, Volume 165, Issue 5, pp 521–532 | Cite as

Quadratically normal and congruence-normal matrices

  • Kh. D. Ikramov
  • H. Fassbender
Article

A matrix AC n×n is unitarily quasidiagonalizable if A can be brought by a unitary similarity transformation to a block diagonal form with 1 × 1 and 2 × 2 diagonal blocks. In particular, the square roots of normal matrices, i.e., the so-called quadratically normal matrices are unitarily quasidiagonalizable. A matrix AC n×n is congruence-normal if \( B = A\overline A \) is a conventional normal matrix. We show that every congruence-normal matrix A can be brought by a unitary congruence transformation to a block diagonal form with 1 × 1 and 2 × 2 diagonal blocks. Our proof emphasizes andexploitsalikenessbetween theequations X 2 = B and \( X\overline X = B \) for a normal matrix B. Bibliography: 13 titles.

Keywords

Russia Similarity Transformation Normal Matrix Diagonal Block Diagonal Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Technische Universität BraunschweigBraunschweigGermany

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