UBC Theses and Dissertations

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UBC Theses and Dissertations

Interlacing inequalities for eigenvalues of sums of matrices Afari, Ernest


We begin with some historical remarks in section 1, where we present the basic interlacing inequalities. In the rest of the thesis we discuss R.C.Thompson's contributions to the subject. His main concern is to extend the inequalities to include more than just one of the (n — 1) x (n — 1) principal submatrices. It is clear that for each such submatrix, the interlacing inequalities are valid, but the resulting set of inequalities is not sufficient to guarantee the existence of a matrix whose principal submatrices have eigenvalues satisfying these inequalities. We have included two examples to show that Thompson's inequalities are necessary.

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