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The Discriminance for <i>FLDcirc<sub>r</sub></i> Matrices and the Fast Algorithm of Their Inverse and Generalized Inverse
College of Science, University of Shanghai for Science and Technology, Shanghai, China
College of Science, University of Shanghai for Science and Technology, Shanghai, China
- 1 College of Science, University of Shanghai for Science and Technology, Shanghai, China
- 2 College of Science, University of Shanghai for Science and Technology, Shanghai, China
Advances in Linear Algebra & Matrix Theory·Volume 05 (2015)·Pages 54–61·Published 9 June 2015·DOI10.4236/alamt.2015.52006
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Abstract
This paper presents a new type of circulant matrices. We call it the first and the last difference r -circulant matrix ( FLDcirc r matrix). We can verify that the linear operation, the matrix product and the inverse matrix of this type of matrices are still FLDcirc r matrices. By constructing the basic FLDcirc r matrix, we give the discriminance for FLDcirc r matrices and the fast algorithm of the inverse and generalized inverse of the FLDcirc r matrices.
Keywords<i>FLDcirc<sub>r</sub></i>MatrixDiscriminanceDiagonalizationInverseGeneralized Inverse
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