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2007•Journal of MathematicsRequires access

ON THE k-GENERALIZED UNITARY MATRICES

Wei Guo

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Abstract

In this paper, the properties of k-generalized unitary matrix and relations between it and unitary matrix, symplectic matrix, Householder matrix are discussed, and many new results are obtained. Moreover, the corresponding results on relations among unitary matrix and Householder matrix are popularized, especially the Cayley decomposition of orthogonal matrix is extended to generalized unitary matrix , and various kinds of the unitary matrices and symplectic matrices are unified.

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What this paper is about

In this paper, the properties of k-generalized unitary matrix and relations between it and unitary matrix, symplectic matrix, Householder matrix are discussed, and many new results are obtained. Moreover, the corresponding results on relations among unitary matrix and Householder matrix are popularized, especially the Cayley decomposition of orthogonal matrix is extended to generalized unitary matrix , and various kinds of the unitary matrices and symplectic matrices are unified.

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Available abstract

In this paper, the properties of k-generalized unitary matrix and relations between it and unitary matrix, symplectic matrix, Householder matrix are discussed, and many new results are obtained. Moreover, the corresponding results on relations among unitary matrix and Householder matrix are popularized, especially the Cayley decomposition of orthogonal matrix is extended to generalized unitary matrix , and various kinds of the unitary matrices and symplectic matrices are unified.

Key concepts: Unitary matrix, Mathematics, Unitary state, Matrix (chemical analysis), Circular ensemble, Symplectic matrix, Symplectic geometry, Pure mathematics

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