[Math] “Sandwich theorem” for eigenvalues of symmetric matrices

Question

I am looking for a reference for the following result for symmetric matrices

Let $A\in\mathbb R^{n\times n}$ be symmetric with eigenvalues
$\lambda_n \leq\ldots\leq\lambda_1,\, M\subset \lbrace 1 \ldots n\rbrace,\, |M|=n-1$ Now let $B\in\mathbb R^{n-1\times n-1},\, B=A(M)$ be the matrix $A$ without the $i$th row and column, where
$i\notin M$

For the eigenvalues $\mu_{n-1} \leq \ldots \leq\mu_1$ of $B$ it holds

$$\lambda_n\leq \mu_{n-1}\leq \lambda_{n-1}\leq\ldots\leq\mu_1\leq\lambda_1 $$

Does anyone know who has proved this first? And maybe a link to the original paper?

Answer 1

It is an application of Courat-Fischer Theorem (or Min-Max Theorem), and here there is a problem on this subject with it's answer