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Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.

5 votes
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Limit of alternated row and column normalizations

When $E_0$ is square (i.e., $r = c$) this procedure is called Sinkhorn iteration or the Sinkhorn-Knopp algorithm (see this Wikipedia page). You can find a wealth of results by Googling those terms, th …
Nathaniel Johnston's user avatar
7 votes
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Solution to a Sylvester equation with positive definite coefficients

This is not true. For example, if $$ A = \begin{bmatrix} 1 & 0 \\ 0 & 4 \end{bmatrix}, B = \begin{bmatrix} 4 & 0 \\ 0 & 1 \end{bmatrix}, C = \begin{bmatrix} 17 & 16 \\ 16 & 17 \end{bmatrix} $$ then ea …
Nathaniel Johnston's user avatar