Basic Properties of Circulant Matrices and Anti-Circular Matrices

Yue, Xiaopeng; Liang, Xiquan

doi:10.2478/v10037-008-0043-x

Abstract

This article introduces definitions of circulant matrices, line-and column-circulant matrices as well as anti-circular matrices and describes their main properties.

MML identifier: MATRIX16, version: 7.9.03 4.108.1028

References

[1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
Search in Google Scholar
[2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
Search in Google Scholar
[3] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
Search in Google Scholar
[4] Czesław Byliński Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
Search in Google Scholar
[5] Katarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.
Search in Google Scholar
[6] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
Search in Google Scholar
[7] Karol Pαk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199-211, 2007.10.2478/v10037-007-0024-5
Search in Google Scholar
[8] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
Search in Google Scholar
[9] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
Search in Google Scholar
[10] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
Search in Google Scholar
[11] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
Search in Google Scholar
[12] Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.
Search in Google Scholar
[13] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.
Search in Google Scholar
[14] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.
Search in Google Scholar

Basic Properties of Circulant Matrices and Anti-Circular Matrices

Abstract

Paradigm

My account