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Matrix Decomposition and Applications | | Jun Lu
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1 Jan 2022 | | Abstract: | In 1954, Alston S. Householder published Principles of Numerical Analysis,
one of the first modern treatments on matrix decomposition that favored a
(block) LU decomposition-the factorization of a matrix into the product of
lower and upper triangular matrices. And now, matrix decomposition has become a
core technology in machine learning, largely due to the development of the back
propagation algorithm in fitting a neural network. The sole aim of this survey
is to give a self-contained introduction to concepts and mathematical tools in
numerical linear algebra and matrix analysis in order to seamlessly introduce
matrix decomposition techniques and their applications in subsequent sections.
However, we clearly realize our inability to cover all the useful and
interesting results concerning matrix decomposition and given the paucity of
scope to present this discussion, e.g., the separated analysis of the Euclidean
space, Hermitian space, Hilbert space, and things in the complex domain. We
refer the reader to literature in the field of linear algebra for a more
detailed introduction to the related fields. | | Source: | arXiv, 2201.00145 | | Services: | Forum | Review | PDF | Favorites | |
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