# Questions tagged [matrices]

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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### Is every matrix involution over a UFD diagonalisable?

Let $A$ be a UFD, that is also a $k$-algebra, where $k$ is a field of characteristic $\not=2$ (for instance polynomials over $k$). Is every involution in $\mathrm{GL}_n(A)$ diagonalisable? This is of ...
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### Lagrange Optimization w.r.t. vector + equality constraint

I am currently facing the following optimization problem: $f(v) = r_f + v'*\mu + v'*diag(\Sigma)*1/2 -v'*\Sigma * v*1/2+(1-\gamma)*v'*\Sigma*v*1/2$ s.t. $1'*v=1$ (sum of the vector elements = 1) ...
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### Product of two involutions in $\mathrm{PSL}_2(D)$

Let $D$ be a division ring and $\mathrm{PSL}_2(D)$. Suppose that $\overline{A}\in\mathrm{PSL}_2(D)$ where $A\in \mathrm{SL}_2(D)$. If $\overline{A}$ is identity, then $\overline{A}$ can express two ...
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