Basic Properties of Circulant Matrices and Anti-Circular Matrices

Xiaopeng Yue; Xiquan Liang

Formalized Mathematics (2008)

  • Volume: 16, Issue: 4, page 355-360
  • ISSN: 1426-2630

Abstract

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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

How to cite

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Xiaopeng Yue, and Xiquan Liang. "Basic Properties of Circulant Matrices and Anti-Circular Matrices." Formalized Mathematics 16.4 (2008): 355-360. <http://eudml.org/doc/266719>.

@article{XiaopengYue2008,
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},
author = {Xiaopeng Yue, Xiquan Liang},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {355-360},
title = {Basic Properties of Circulant Matrices and Anti-Circular Matrices},
url = {http://eudml.org/doc/266719},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Xiaopeng Yue
AU - Xiquan Liang
TI - Basic Properties of Circulant Matrices and Anti-Circular Matrices
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 4
SP - 355
EP - 360
AB - 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
LA - eng
UR - http://eudml.org/doc/266719
ER -

References

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  6. [6] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. 
  7. [7] Karol Pαk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199-211, 2007. 
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  9. [9] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990. 
  10. [10] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  11. [11] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  12. [12] Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005. 
  13. [13] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992. 
  14. [14] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993. 

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