Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
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According to the characterization of eigenvalues of a real symmetric matrix A, the largest eigenvalue is given by the maximum of the quadratic form 驴xA, x驴 over the unit sphere; the second largest eigenvalue of A is given by the maximum of this same quadratic form over the subset of the unit sphere consisting of vectors orthogonal to an eigenvector associated with the largest eigenvalue, etc. In this study, we weaken the conditions of orthogonality by permitting the vectors to have a common inner product r where 0 驴 r