Abstract
In this paper, we study a new L2 norm preserving heat flow in matrix geometry. We show that if the initial data has trace zero and has unit L2 norm, this flow has a global solution and enjoys the entropy stability in any finite time. We show that as the time is approaching infinity, the flow has its limit as an eigen-matrix of the Laplacian operator. Interesting operator convex property of heat equation is also derived.
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