منابع مشابه
A determinantal inequality for positive semidefinite matrices
Let A,B,C be n× n positive semidefinite matrices. It is known that det(A+ B + C) + detC ≥ det(A+ C) + det(B + C), which includes det(A+B) ≥ detA+ detB as a special case. In this article, a relation between these two inequalities is proved, namely, det(A+ B + C) + detC − (det(A+ C) + det(B + C)) ≥ det(A+ B)− (detA+ detB).
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We prove that for positive semidefinite matrices A and B the eigenvalues of the geometric mean A#B are log-majorised by the eigenvalues of A1/2B1/2. From this follows the determinantal inequality det(I + A#B) ≤ det(I + A1/2B1/2). We then apply this inequality to the study of interpolation methods in diffusion tensor imaging.
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We study a special class of irreducible representations of GLn over a local non-Archimedean field which we call ladder representations. This is a natural class in the admissible dual which contains the Speh representations. We show that the Tadić determinantal formula is valid for this class and analyze the standard modules pertaining to these representations.
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We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman’s complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when the complex resolves a maximal Cohen-Macaulay module supported on the quiver determinantal variety. This allows us to find the set-theoretical defining equat...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1994
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)90108-2