منابع مشابه
Categorical aspects of polar decomposition
Polar decomposition unquestionably provides a notion of factorization in the category of Hilbert spaces. But it does not fit existing categorical notions, mainly because its factors are not closed under composition. We observe that the factors are images of functors. This leads us to consider notions of factorization that emphasize reconstruction of the composite category from the factors. We f...
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The polar decomposition of a square matrix has been generalized by several authors to scalar products on Rn or Cn given by a bilinear or sesquilinear form. Previous work has focused mainly on the case of square matrices, sometimes with the assumption of a Hermitian scalar product. We introduce the canonical generalized polar decomposition A = WS, defined for general m × n matrices A, where W is...
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General properties of the spin motion in e+estorage rings are studied in order to determine the conditions where radiative beam polarization is likely to occur. A general first-order theory of depolarization is developed and applied to specific examples of nonresonant , depolarization in storage rings. It is found that under many practical conditions radiative beam polarization should occur and...
متن کاملPolar decomposition and Brion’s theorem
In this note we point out the relation between Brion’s formula for the lattice point generating function of a convex polytope in terms of the vertex cones [Bri88] on the one hand, and the polar decomposition à la Lawrence/Varchenko [Law91a, Var87] on the other. We then go on to prove a version of polar decomposition for non-simple polytopes.
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General 3×3 linear or 4×4 homogenous matrices can be formed by composing primitive matrices for translation, rotation, scale, shear, and perspective. Current 3-D computer graphics systems manipulate and interpolate parametric forms of these primitives to generate scenes and motion. For this and other reasons, decomposing a composite matrix in a meaningful way has been a longstanding challenge. ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.12.013