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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

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Maximizing a vector after a series of matrix multiplications

Problem Statement Let's say we have a set of $n\times n$ matrices $X=\{M_1,\ldots,M_r\}$ and weights of these matrices $\{w_1,\ldots,w_r\}$ along with a set of "initial vectors" $\{v_1,\ldots,v_s\}$. …
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Finding which members of a family of (possibly infinite-dimensional) matrices have trivial n...

Background I have a set $S$ (that is possibly infinite) and a correspondence between functions $c:S^3\to\mathbb{R}$ (I will write $c(i,j,k)$ as $c_{ijk}$) and matrices $M$ with rows indexed by $(i,j,k …
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  • 509