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What is Singular Value Decomposition mean?
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any m × n {\displaystyle m\times n} matrix. It is related to the polar decomposition.
Specifically, the singular value decomposition of an m × n {\displaystyle m\times n} complex matrix M is a factorization of the form U Σ V ∗ {\displaystyle \mathbf {U\Sigma V^{*}} } , where U is an m × m {\displaystyle m\times m} complex unitary matrix, Σ {\displaystyle \mathbf {\Sigma } } is an m × n {\displaystyle m\times n} rectangular diagonal matrix with non-negative real numbers on the diagonal, and V is an n × n {\displaystyle n\times n} complex unitary matrix. If M is real, U and V can also be guaranteed to be real orthogonal matrices. In such contexts, the SVD is often denoted U Σ V T {\displaystyle \mathbf {U\Sigma V^{T}} } .
The diagonal entries σ i reference
Posted on 05 Nov 2024, this text provides information on Miscellaneous in Electronics related to Electronics. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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