Journal of Mathematical Sciences

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

Quadratically normal and congruence-normal matrices

Article

A matrix ACn×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 ACn×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 X2 = B and \( X\overline X = B \) for a normal matrix B. Bibliography: 13 titles.

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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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