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54 votes
5 answers
2k views

Unusual symmetries of the Cayley-Menger determinant for the volume of tetrahedra

Suppose you have a tetrahedron $T$ in Euclidean space with edge lengths $\ell_{01}$, $\ell_{02}$, $\ell_{03}$, $\ell_{12}$, $\ell_{13}$, and $\ell_{23}$. Now consider the tetrahedron $T'$ with edge ...
Dylan Thurston's user avatar
13 votes
1 answer
1k views

When is a matrix similar to a non-negative matrix?

Consider a real square matrix $A$ of size $n\times n$. Under which conditions on $A$ does there exist a row-stochastic matrix $U$ (non-negative, rowsums = 1), such that $A'=U^{-1}AU$ is a non-negative ...
J Reichardt's user avatar