A.S. Lewis. Convex analysis on Cartan subspaces. Nonlinear Analysis, Theory, Methods and Applications, 42:813-820, 2000. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Generalized Schur-concave functions and Eaton triples - Tin-Yau Tam Department (Correct)
....the preordering #G to that of #H where H is a finite reflection group, when any one of the conditions is met. In this event, we call the Eaton triple (W, H,F ) in Theorem 1 a reduced triple of (V, G, F ) See [20] for the relation between Eaton triples and Lewis normal decomposition systems [12]. Let # be a root system of the finite reflection group H # O(W ) which is the orthogonal group on W where (W, H, F ) is a reduced triple of the Eaton triple (V, G, F ) Since F is a fundamental domain and thus Int W F , the interior of F in W (a fundamental region [5] determines a positive ....
A.S. Lewis, Convex analysis on Cartan subspaces, Nonlinear Anal., 42 (2000), 813-820.
The Mathematics Of Eigenvalue Optimization - Lewis (2003) (1 citation) Self-citation (Lewis) (Correct)
....any familiarity with Lie theory, we simply retrace our steps through the familiar case of symmetric matrices, using the key results as illustrations of the general case. For this beautiful classical development we follow the outline provided by [53, Chap. 5, Sec. 3,4] More details appear in [40]. We begin with our familiar decomposition of the vector space of n by n real matrices with trace zero, sl(n; R) into a sum of the subspace of skew symmetric matrices, so(n) and the symmetric matrices with trace zero, pn , and note this sum is direct and orthogonal with respect to the bilinear ....
....from Horn s result. Von Neumann s characterization has an analogous restatement: a unitarily invariant function on M is a norm if and only if its restriction to the Euclidean subspace of real diagonal matrices, D , is a norm. Using Kostant s theorem, we obtain the following broad uni cation [40]. Corollary 5.3 (invariant convex functions) In the framework of Kostant s theorem, a K invariant function h : p R is convex if and only if its restriction to the subspace a is convex. Von Neumann s characterization follows by considering the standard Cartan decomposition of the Lie algebra ....
[Article contains additional citation context not shown here]
A.S. Lewis. Convex analysis on Cartan subspaces. Nonlinear Analysis, Theory, Methods and Applications, 42:813-820, 2000.
Hyperbolic Polynomials and Convex Analysis - Bauschke, Güler, Lewis, Sendov (1998) (2 citations) Self-citation (Lewis) (Correct)
....matrix norms as symmetric gauge functions of the singular values. Indeed, the analogy is not accidental: the paper [19] develops an axiomatic framework subsuming both models, and at a more sophisticated level, both results follow quickly from the Kostant convexity theorem in semisimple Lie theory [20]. The work we describe in this current paper also concerns the above type of convexity result, but with a very different and remarkably simple approach. To illustrate the key idea, consider the determinant as a function on S n . This function is a homogeneous polynomial which is hyperbolic with ....
A.S. LEWIS. Convex analysis on Cartan subspaces, April 1997. Preprint.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC