P. Binding and C. K. Li. Joint ranges of hermitian matrices and simultaneous diagonalization. Linear Algebra and its Applications, 151:157--167, 1991. Home/Search Document Not in Database Summary Related Articles Check |
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Polyhedra, Spectrahedra, and Semidefinite Programming - Ramana (1997) (Correct)
....X T Q a (x)X = Q a (x) 0 0 D(x) where D(x) is a k Theta k diagonal affine matrix map (k n) and S = fxjD ii (x) 0 8 i = 1; kg. It should be mentioned that, similar results have been established in the context of convexity and polyhedrality of ranges of quadratic maps in [3] and [2] However, a relatively direct application of the results of those articles to our situation does not seem evident. The following example shows that the assumption of full dimensionality is not dispensable. Example 1: Let Q a (x) 1 x 1 x 1 x 1 0 : Clearly, S = fxjQ a ....
P. Binding and C-K. Li, Joint ranges of Hermitian matrices and simultaneous diagonalization, Linear Algebra and its Applications, Vol. 151, pp. 157-167, 1991.
Convexity of the Joint Numerical Range - Li, Poon (1998) Self-citation (Li) (Correct)
....matrices. For 1 k n, the kth joint numerical range of A is defined as W k (A) f(tr (X A 1 X) tr (X AmX) X 2 C n Thetak ; X X = I k g: When k = 1, it reduces to the usual joint numerical range of A that are useful in the study of various pure and applied subjects (see [2, 3, 4, 5, 7]) In particular, in the study of structured singular values arising in robust stability (see [6, 7, 15] it is important that W 1 (A) is convex. Unfortunately, W 1 (A) is not always convex if m 3 (e.g. see [1] We modify the example in [1] to show that the same conclusion holds for W k (A) ....
P. Binding and C.K. Li, Joint ranges of Hermitian matrices and simultaneous diagonalization, Linear Algebra Appl. 151 (1991), 157-168.
Optimal Solutions to the Inverse Problem in Quadratic Magnetic .. - Of The School (Correct)
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P. Binding and C. K. Li. Joint ranges of hermitian matrices and simultaneous diagonalization. Linear Algebra and its Applications, 151:157--167, 1991.
Some Geometric Results in Semidefinite Programming - Ramana, Goldman (1995) (7 citations) (Correct)
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P. Binding and C-K. Li, Joint Ranges of Hermitian Matrices and Simultaneous Diagonalization, Linear Algebra Appl. 151 (1991), pp. 157-167.
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