The minimax principle for j involves j-dimensional subspaces Sj : Equivalent to equation
Chapter 6, Problem 6.4.13(choose chapter or problem)
The minimax principle for j involves j-dimensional subspaces Sj : Equivalent to equation (15) j = min Sj max x in Sj R(x) . (a) If j is positive, infer that every Sj contains a vector x with R(x) > 0. (b) Deduce that Sj contains a vector y = C 1 x with y T c TACy/y T y > 0. (c) Conclude that the jth eigenvalue of C TAC, from its minimax principle, is also positiveproving again the law of inertia in Section 6.2.
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