Can we determine the number of positive eigenvalues for the following tridiagonal matrix under some criterion in terms of $a_i,b_i,c_i$: $$ A_n= \begin{pmatrix} a_{1} & b_{1} \\\ c_{1} & a_{2} & b_{2} \\\ & c_{2} & a_{3} & \ddots \\\ & & \ddots & \ddots & b_{n-1} \\\ & & & c_{n-1} & a_{n} \end{pmatrix} $$
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$\begingroup$ This question is inspired by matters at mathoverflow.net/questions/131527/… $\endgroup$– David Roberts ♦Commented Jul 1 at 4:34
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