Let be a sequence of symmetric matrices of increasing order with , 2, ..., and , 2, ..., . Let be the th eigenvalue of for , 2, ..., , where the ordering is given by
Then it follows that
Let be a sequence of symmetric matrices of increasing order with , 2, ..., and , 2, ..., . Let be the th eigenvalue of for , 2, ..., , where the ordering is given by
Then it follows that
Weisstein, Eric W. "Sturmian Separation Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SturmianSeparationTheorem.html