Matrix Theory pp 131-158 | Cite as

Unitary Matrices and Contractions

  • Fuzhen Zhang
Part of the Universitext book series (UTX)


This chapter studies unitary matrices and contractions. Section 5.1 gives basic properties of unitary matrices, Section 5.2 discusses the structure of real orthogonal matrices under similarity, and Section 5.3 develops metric spaces and the fixed-point theorem of strict contractions. Section 5.4 deals with the connections of contractions with unitary matrices, Section 5.5 concerns the unitary similarity of real matrices, and Section 5.6 presents a trace inequality for unitary matrices, relating the average of the eigenvalues of each of two unitary matrices to that of their product.


Convex Combination Real Matrix Unitary Matrice Unitary Similarity Trace Inequality 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Fuzhen Zhang
    • 1
  1. 1.Department of Math, Science, and TechnologyNova Southeastern UniversityFort LauderdaleUSA

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