Displaying similar documents to “Linear transforms and convolution”

Linear transforms supporting circular convolution over a commutative ring with identity

Mohamed Mounir Nessibi (1995)

Commentationes Mathematicae Universitatis Carolinae

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We consider a commutative ring R with identity and a positive integer N . We characterize all the 3-tuples ( L 1 , L 2 , L 3 ) of linear transforms over R N , having the “circular convolution” property, i.eṡuch that x * y = L 3 ( L 1 ( x ) ⊗ L 2 ( y ) ) for all x , y ∈ R N .

An inverse matrix of an upper triangular matrix can be lower triangular

Waldemar Hołubowski (2002)

Discussiones Mathematicae - General Algebra and Applications

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In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.

Representation of doubly infinite matrices as non-commutative Laurent series

María Ivonne Arenas-Herrera, Luis Verde-Star (2017)

Special Matrices

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We present a new way to deal with doubly infinite lower Hessenberg matrices based on the representation of the matrices as the sum of their diagonal submatrices. We show that such representation is a simple and useful tool for computation purposes and also to obtain general properties of the matrices related with inversion, similarity, commutativity, and Pincherle derivatives. The diagonal representation allows us to consider the ring of doubly infinite lower Hessenberg matrices over...