The largest singular value of e/sup X/A/sub 0/e/sup -X/ is convex on convex sets of commuting matrices

A short and direct proof of the convexity property is given. It is shown that the theorem applies to any convex, commuting set of matrices in R/sup nXn/, where A/sub 0/ in R/sup nXn/ is fixed. It is also shown that the result does not hold if X is permitted to be a general square matrix. A counterexample is supplied for noncommuting matrices.<
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