A Convexity Question in Matrix Analysis (Open)

Summary: The reader is asked to prove that for a real matrix $B$ with maximal rank $m \le n$, in the orthant where each $\lambda_i$ is positive, the scalar-valued function ${\cal C}(\lambda_1, \ldots, \lambda_n) = Tr((B^{\ast}\diag(\lambda_1, \ldots, \lambda_n) B)^{-2})$ is convex.

Classification: Primary, Algebra; Secondary, Matrices and Determinants

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David L. Russell
Mathematics Department
Virginia Tech
Blacksburg, VA 24061-0123
e-mail: russell@math.vt.edu

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