## Abstract and Applied Analysis

### Invertibility and Explicit Inverses of Circulant-Type Matrices with $k$-Fibonacci and $k$-Lucas Numbers

#### Abstract

Circulant matrices have important applications in solving ordinary differential equations. In this paper, we consider circulant-type matrices with the $k$-Fibonacci and $k$-Lucas numbers. We discuss the invertibility of these circulant matrices and present the explicit determinant and inverse matrix by constructing the transformation matrices, which generalizes the results in Shen et al. (2011).

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 238953, 9 pages.

Dates
First available in Project Euclid: 3 October 2014

https://projecteuclid.org/euclid.aaa/1412361157

Digital Object Identifier
doi:10.1155/2014/238953

Mathematical Reviews number (MathSciNet)
MR3214409

Zentralblatt MATH identifier
07021976

#### Citation

Jiang, Zhaolin; Gong, Yanpeng; Gao, Yun. Invertibility and Explicit Inverses of Circulant-Type Matrices with $k$ -Fibonacci and $k$ -Lucas Numbers. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 238953, 9 pages. doi:10.1155/2014/238953. https://projecteuclid.org/euclid.aaa/1412361157

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