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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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The expected square of the determinant of a random row stochastic matrix
Not a full answer.
The determinant of an $n\times n$ matrix $A$ is the volume of the parallelotope spanned by its rows. That volume is equal to $n!$ times the volume of the $n$-simplex whose vertices …