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The largest singular value of eXA0e -X is convex on convex sets of commuting matrices

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2 Author(s)
Sezginer, R.S. ; Courant Inst. of Math. Sci., New York Univ., NY, USA ; Overton, M.L.

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 RnXn, where A0RnXn 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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Automatic Control, IEEE Transactions on  (Volume:35 ,  Issue: 2 )