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On a singular set for the restriction of the characteristic map to a linear subspace of $$\mathcal M_n$$. (English) Zbl 1078.15014
The author uses a topological language to give basic characterizations of the set of matrices $$\mathbf A \in \mathcal M_n$$ (over an algebraically closed field $$\mathbf F$$ of characteristic zero) such that the image $$\chi _{\mathbf A}(\mathcal L)$$ is not dense in $$\mathbf F^n$$, where $$\mathcal L\subseteq \mathcal M_n$$ is a fixed linear subspace and $$\chi _{\mathbf A}\:\mathcal M_n \to \mathbf F^n$$ is the characteristic map associated with $$\mathbf A$$. The case $$n\in \{2,3\}$$ is studied in more detail.
MSC:
 15A30 Algebraic systems of matrices 15A18 Eigenvalues, singular values, and eigenvectors
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References:
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