Efficient algorithm for finding the inverse and the group inverse of FLSr-circulant matrix
Copyright policy )Efficient algorithm for finding the inverse and the group inverse of FLSr-circulant matrix
FLS \(r\)-circulant and FLS \(r\)-retrocirculant matrices are defined. Based on the proved theorems algorithms are deduced for the computation of the inverse or group inverse of regular and singular FLS \(r\)-circulant matrices, respectively, using representations of the matrices and the Euclidean algorithm. The inverse of the FLS \(r\)-retrocirculant matrix can be computed using an established relationship between the two matrix types. Two examples are given, one for a nonsingular and another for a singular matrix.
- Xi’an Jiaotong-Liverpool University China (People's Republic of)
- Qufu Normal University China (People's Republic of)
polynomial ring, numerical examples, Numerical solutions to overdetermined systems, pseudoinverses, group inverse, FLS \(r\)-retrocirculant matrix, Canonical forms, reductions, classification, inverse, Hermitian, skew-Hermitian, and related matrices, Direct numerical methods for linear systems and matrix inversion, FLS \(r\)-circulant matrix, Euclidean algorithm
polynomial ring, numerical examples, Numerical solutions to overdetermined systems, pseudoinverses, group inverse, FLS \(r\)-retrocirculant matrix, Canonical forms, reductions, classification, inverse, Hermitian, skew-Hermitian, and related matrices, Direct numerical methods for linear systems and matrix inversion, FLS \(r\)-circulant matrix, Euclidean algorithm
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