Unitary Matrices and Contractions
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This chapter studies unitary matrices and contractions. Section 6.1 gives basic properties of unitary matrices, Section 6.2 discusses the structure of real orthogonal matrices under similarity, and Section 6.3 develops metric spaces and the fixed-point theorem of strict contractions. Section 6.4 deals with the connections of contractions with unitary matrices, Section 6.5 concerns the unitary similarity of real matrices, and Section 6.6 presents a trace inequality for unitary matrices, relating the average of the eigenvalues of each of two unitary matrices to that of their product.
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