A further note on max-min properties of matrix factor norms
- Siemens Research Corp., Princeton, NJ (United States)
- New York Univ., New York, NY (United States). Courant Inst. of Mathematical Sciences
In a previous paper (SIAM J. Sci. Comput., 15 (1994), pp. 348-358) the authors considered the following problem: given a set of real matrices A{sub 1},...,A{sub k}, under what conditions does the equality as given by equation (1) in the paper hold. It was shown that if the matrices A{sub j}, j = 1,...,k are normal and commute with one another then the equality holds, but a 2-by-2 example was given to show that for noncommuting matrices the equality may fail for k > 1. For the given example, however, it was pointed out by L.N. Trefethen that equality does hold if one considers the maximum over all complex vectors w. In this paper it is shown that for 2-by-2 real symmetric matrices, when the vectors w and coefficients a{sub 1},...,a{sub k} are allowed to be complex, if the left-hand side of (1) is equal to 1, then the right-hand side is also equal to 1. It is shown that for matrices of dimension 3 or greater, however, one can construct examples in which the left-hand side of (*) is equal to 1 and the right-hand side is strictly less than 1.
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- FG02-88ER25053
- OSTI ID:
- 32071
- Journal Information:
- SIAM Journal on Scientific Computing, Vol. 16, Issue 2; Other Information: PBD: Mar 1995
- Country of Publication:
- United States
- Language:
- English
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