Approximate Solution of Integral Equations and Differential Equations

Abstract

If $\sum\limits_{i = 1}^s {\sum\limits_{j = 1}^s {{\alpha_{ij}}{x_i}{x_j}\left( {{\alpha_{ij}} = {\alpha_{ji}}} \right)} }$ is a semi-positive definite quadratic form, then

$$ 0 \leqslant \det \left( {{\alpha_{ij}}} \right) \leqslant \prod\limits_{i = 1}^s {{\alpha_{ii}}} $$

.