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Results tagged with matrices
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user 161725
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
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For which sets of linearly independent complex matrices does there exist a vector whose imag...
Hence, it is natural to ask for additional constraints on the given matrices which allow the required vector to exist. … For instance, if we demand that the matrices are diagonalizable and mutually commuting, then there exists a common eigenbasis $\{w_i\}_{i=1}^d$ of $\mathbb{C}^d$ in which all the matrices are diagonal. …
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When does a matrix subspace contain a full rank matrix?
Cross-posted at Math SE
Let $S\subseteq M_{n,m}(\mathbb{C})$ be a $d$-dimensional subspace of the space of $n\times m$ complex matrices (with $n\leq m$, say). …
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