Abstract
Matrix factorizations or matrix decompositions are methods that represent a matrix as a product of two or more matrices. There are various types of matrix factorizations such as LU factorization, Cholesky factorization, singular value decomposition etc. Matrix factorization is widely used in pattern recognition, image denoising, data clustering etc. Motivated by these applications, some properties and applications of various types of matrix factorizations are studied. One of the purposes of matrix factorization is to ease the computation. Thus, comparisons in term of computation time of various matrix factorizations in different areas are carried out.
Highlights
Matrix factorizations or matrix decompositions are methods that represent a matrix as a product of two or more matrices
Matrix factorization is usually used to simplify the computations in solving a problem which is relatively difficult to solve in its original form
From the results shown in the three tables above, we found that Cholesky factorization is the most efficient way in solving the linear system when A is Hermitian
Summary
Matrix factorizations or matrix decompositions are methods that represent a matrix as a product of two or more matrices. We list the notations and definitions used in this paper
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