Sturmian Separation Theorem

Let A_r=a_(ij) be a sequence of N symmetric matrices of increasing order with i,j=1, 2, ..., r and r=1, 2, ..., N. Let lambda_k(A_r) be the kth eigenvalue of A_r for k=1, 2, ..., r, where the ordering is given by


Then it follows that


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Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1121, 2000.

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Sturmian Separation Theorem

Cite this as:

Weisstein, Eric W. "Sturmian Separation Theorem." From MathWorld--A Wolfram Web Resource.

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