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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

8 votes
2 answers
5k views

Lipschitz constant of a function of matrix

The function is given by $f(X) = (AX^{-1}A^\top + B)^{-1}$ where $X$, $A$, and $B$ are $n \times n$ positive definite matrices. I'm trying to find the Lipschitz constant such that $\| f(X)-f(Y) \| \ …