MathLiveSingular value decomposition
Factorizes any complex m-by-n matrix into a product of a unitary matrix, a diagonal matrix of non-negative singular values, and the conjugate transpose of another unitary matrix. It is used in dimensionality reduction, least squares, pseudoinverses, and numerical rank computation.
M = U \Sigma V^*What the symbols mean
| the original m×n matrix being decomposed | |
| an m×m unitary matrix whose columns are the left singular vectors | |
| an m×n diagonal matrix with non-negative real singular values on the diagonal | |
| the conjugate transpose of the n×n unitary matrix V, whose columns are the right singular vectors |
About this formula
- FieldMathematics
- TopicLinear algebra
- LevelUniversity
- Also calledSVD, matrix factorization, singular value decomposition formula, decompose matrix into singular values, U sigma V* decomposition, SVD of a matrix
- SourceWikidata Q420904
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