Applications of singular-value decomposition (SVD)

Alkiviadis G. Akritas and Gennadi I. Malaschonok

Mathematics and Computers in Simulation (MATCOM), 2004, vol. 67, issue 1, 15-31

Abstract: Let A be an m×n matrix with m≥n. Then one form of the singular-value decomposition of A is A=UTΣV,where U and V are orthogonal and Σ is square diagonal. That is, UUT=Irank(A), VVT=Irank(A), U is rank(A)×m, V is rank(A)×n and Σ=σ10⋯000σ2⋯00⋮⋮⋱⋮⋮00⋯σrank(A)−1000⋯0σrank(A)is a rank(A)×rank(A) diagonal matrix. In addition σ1≥σ2≥⋯≥σrank(A)>0. The σi’s are called the singular values of A and their number is equal to the rank of A. The ratio σ1/σrank(A) can be regarded as a condition number of the matrix A.

Keywords: Applications; Singular-value decompositions; Hanger; Stretcher; Aligner (search for similar items in EconPapers)
Date: 2004
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:67:y:2004:i:1:p:15-31

DOI: 10.1016/j.matcom.2004.05.005

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