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A set of real numbers $\{\lambda_1, \dots, \lambda_n \}$, $n \geq 1$, is called a Suleĭmanova spectrum if it contains exactly one positive value and $\sum_{i=1}^n \lambda_i \geq 0$. (It is well-known ...

Let $A\in\mathcal M_n$ be an $n\times n$ real [symmetric] matrix which depends smoothly on a [finite] set of parameters, $A=A(\xi_1,\ldots,\xi_k)$. We can view it as a smooth function $A:\mathbb R^k\...