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Let $v_1, \cdots, v_n$ be vectors in $\mathbb R^k$, and let $M$ be the Gram matrix of them. It's possible to determine from $M$ and $k$ whether the only vector that has nonnegative inner product with ...

I recently stumbled upon a well-known version of Farkas' Lemma which, roughly speaking, I would like to generalize from real vectors to hermitian matrices, as it seems promising for something else I ...

I am considering $$ \min_{M\in \mathcal{M}} \|X - M\|:=x \neq 0, $$ where $X$, $M$ are $m\times n$ matrices, $\|\cdot\|$ is spectral norm and $\mathcal{M}$ is a matrix subspace. I wonder to what ...