Convex maps on $\protect \mathbb{R}^n$ and positive definite matrices
We obtain several convexity statements involving positive definite matrices. In particular, if $A,B,X,Y$ are invertible matrices and $A,B$ are positive, we show that the map \[ (s,t) \mapsto \mathrm{Tr}\,\log \left(X^*A^sX + Y^*B^tY\right) \] is jointly convex on $\mathbb{R}^2$. This is related to s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2020-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.25/ |