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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.
15A30 Algebraic systems of matrices
15A18 Eigenvalues, singular values, and eigenvectors
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