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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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characterize certain type of matrices
I'm guessing that these don't have a name, as they are fairly degenerate matrices.
If more than two of the $c_i$ are nonzero, then no matrices satisfy these criteria. … If two of the $c_i$ are nonzero, then all such matrices of this form have two columns $j, j'$ with nonzero entries and have $M_{ij}/M_{ij'}$ going through all $n^{th}$ roots of some nonzero complex number …