Question: Let the p q matrix A, with components a r i , be considered as defining a linear transformation from the domain, R q,

Let the p × q matrix A, with components a r

, be considered as defining a linear transformation from the domain, R q, to the range in R p. Interpret the singular values of A as invariants under independent orthogonal transformation of the domain and range spaces. For the definition of singular values and their application in numerical linear algebra, see Chambers (1977, Section 5.e).

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