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Results tagged with linear-algebra
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user 15506
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
11
votes
Accepted
Relating a Polynomial equation to the characteristic equation of a Hermitian matrix
Let $K$ be a subfield of $\mathbb R$ (e.g., $K=\mathbb Q$) and $f\in K[x]$ be a monic polynomial of degree $n$ all of whose roots are real. We want to compute a symmetric matrix $A\in K^{n\times n}$ s …
8
votes
Accepted
Quadratic Farkas' Lemma?
Here is a counterexample: Take $n=2$ variables $X$ and $Y$. Let $L_1,\dots,L_5$ be linear polynomials such that
$$S:=\{ (x, y) \in {\mathbb R}^2 ~|~ L_i(x,y) \ge 0\}$$ is a pentagon inscribed in the …