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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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What does multiplying a matrix by its transpose have to do with spectral theorem?
In the finite dimensional case the Spectral Theorem says that we can decompose a self-adjoint operator into a sum of projection operators: if $A$ is self-adjoint then we can write
$A=\lambda_{1}P_{1} …