This paper presents a new approach for representing multidimensional data by a compact
number of bases. We consider the multidimensional data as tensors instead of matrices or …

We study two different techniques for the computation of a matrix inverse, the traditional
approach based on Gaussian factorization and the Gauss-Jordan elimination alternative …

Singular value decomposition (SVD) is one of the most useful matrix decompositions in
linear algebra. Here, a novel application of SVD in recovering ripped photos was exploited …

This paper presents a detailed discussion of the Kronecker product of matrices. It begins
with the definition and some basic properties of the Kronecker product. Statements will be …

This research introduces a row compression and nested product decomposition of an nxn
hierarchical representation of a rank structured matrix A, which extends the compression …

A new and powerful method for matrix decomposition is developed in this work. It is similar
to singular value decomposition and the main idea comes from the univariate approximation …

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In this paper we develop the notion of a generalized matrix product that includes in its
formulation the common matrix and vector products of linear algebra. After defining the …

Some of important methods for signal processing, such as principal component analysis
(PCA), independent component analysis (ICA), non-negative matrix factorization (NMF), and …

Discrete unitary transforms are extensively used in many signal processing applications,
and in the development of fast algorithms Kronecker products have proved quite useful. In …