Polar and Singular Value Decomposition Theorems

摘要: There exists a very powerful set of techniques for dealing with sets equations or matrices that are either singular numerically close to singular. In many cases where Gaussian elimination and triangle decomposition fail give satisfactory results, this techniques, known as value (SVD) will solve it, in the sense giving you useful numerical answer. chapter, reader see SVD any matrix is always realizable. Applications [and related tool polar (PD), canonical factorization, generalizing complex number’s factorization by its modulus phase factor] not restricted analysis; other application examples presented chapter. More advanced readers who wish familiarize themselves infinite-dimensional versions PD their various applications may consult guide literature provided.