Abstract and Applied Analysis

The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and g -Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers

Zhaolin Jiang and Dan Li

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Abstract

Circulant matrices play an important role in solving delay differential equations. In this paper, circulant type matrices including the circulant and left circulant and g -circulant matrices with any continuous Fibonacci and Lucas numbers are considered. Firstly, the invertibility of the circulant matrix is discussed and the explicit determinant and the inverse matrices by constructing the transformation matrices are presented. Furthermore, the invertibility of the left circulant and g -circulant matrices is also studied. We obtain the explicit determinants and the inverse matrices of the left circulant and g -circulant matrices by utilizing the relationship between left circulant, g -circulant matrices and circulant matrix, respectively.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 931451, 14 pages.

Dates
First available in Project Euclid: 3 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412360626

Digital Object Identifier
doi:10.1155/2014/931451

Mathematical Reviews number (MathSciNet)
MR3246367

Zentralblatt MATH identifier
07023336

Citation

Jiang, Zhaolin; Li, Dan. The Invertibility, Explicit Determinants, and Inverses of Circulant and Left Circulant and $g$ -Circulant Matrices Involving Any Continuous Fibonacci and Lucas Numbers. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 931451, 14 pages. doi:10.1155/2014/931451. https://projecteuclid.org/euclid.aaa/1412360626


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