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$A= (a_{ij})$ is an $n\times n$ symmetric positive matrix. It induces a quadratic form $f(x):= x^tAx$ on $\mathbb{R}^n$. $D_m$ denotes the determinant of the top left $m\times m$ submatrix of $A$ (or ...

In a work about the Wave Equation, I encountered the following symmetric matrix of size $1+n$, whose entries are quadratic forms. The arguments are a scalar $a$ and a vector $X\in k^n$. $$S(a,X)=\...

A paper I'm reading in representation theory states the following result: Let $F$ be a field of characteristic zero, and $x$ a symmetric matrix in $M_n(F)$ all of whose principal minors are not zero. ...