2009Journal of Shaanxi University of TechnologyRequires access

On the properties and generalized inverse of (-1)-circulant matrix

Yan Lie-ya

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Abstract

Many studies on the property and application of circulant matrices have been made,but the discussions of(-1)-circulant matrices are less comparatively.(1)-circulant matrix and circulant matrix have close connection.In this paper,by means of properties of circulant matrices,a few properties of(-1)-circulant matrices are discussed,a block diagonalized form is obtained on(-1)-circulant matrices by unitary similarity,and property of generalized inverse on(-1)-circulant matrices is given.

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Many studies on the property and application of circulant matrices have been made,but the discussions of(-1)-circulant matrices are less comparatively.(1)-circulant matrix and circulant matrix have close connection.In this paper,by means of properties of circulant matrices,a few properties of(-1)-circulant matrices are discussed,a block diagonalized form is obtained on(-1)-circulant matrices by unitary similarity,and property of generalized inverse on(-1)-circulant matrices is given.

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Available abstract

Many studies on the property and application of circulant matrices have been made,but the discussions of(-1)-circulant matrices are less comparatively.(1)-circulant matrix and circulant matrix have close connection.In this paper,by means of properties of circulant matrices,a few properties of(-1)-circulant matrices are discussed,a block diagonalized form is obtained on(-1)-circulant matrices by unitary similarity,and property of generalized inverse on(-1)-circulant matrices is given.

Key concepts: Circulant matrix, Mathematics, Inverse, Matrix (chemical analysis), Pure mathematics, Combinatorics, Integer matrix, Complex Hadamard matrix

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