Abstract
We assume that the reader is familiar with the contents of a standard course in linear algebra, including finite-dimensional vector spaces, subspaces, linear transformations and matrices, determinants, eigenvalues, bilinear and quadratic forms, positive definiteness, inner product spaces, and orthogonal linear transformations. Accounts of these topics may be found in most linear algebra books (e.g., [14] or [21]). Throughout the book V will denote a real Euclidean vector space, i.e., a finite-dimensional inner product space over the real field ℛ. Partly in order to establish notation we list some of the properties of V that are of importance for the ensuing discussion.
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