A Simple Proof of the Polar Decomposition Theorem
نویسندگان
چکیده
منابع مشابه
A simple proof of Kashin’s decomposition theorem∗†
Compressive Sensing techniques are used in a short proof of Kashin’s decomposition theorem generalized to `p-spaces for p ≤ 1. The proof is based on the observation that the null-space of a properly-sized matrix with restricted isometry property is almost Euclidean when endowed with the `p-quasinorm. Kashin’s decomposition theorem states that, for any integer m ≥ 1, `2m 1 is the orthogonal sum ...
متن کاملA Simple Proof of the BPH Theorem
A new formalism is given for the renormalization of quantum field theories to all orders of perturbation theory, in which there are manifestly no overlapping divergences. We prove the BPH theorem in this formalism, and show how the local subtractions add up to counterterms in the action. Applications include the renormalization of lattice perturbation theory, the decoupling theorem, Zimmermann ...
متن کاملA simple proof of Zariski's Lemma
Our aim in this very short note is to show that the proof of the following well-known fundamental lemma of Zariski follows from an argument similar to the proof of the fact that the rational field $mathbb{Q}$ is not a finitely generated $mathbb{Z}$-algebra.
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.
متن کاملSimple proof of Chebotarëv’s theorem
We give a simple proof of Chebotarëv’s theorem: Let p be a prime and ω a primitive pth root of unity. Then all minors of the matrix ( ω ij )p−1 i,j=0 are non-zero. Let p be a prime and ω a primitive pth root of unity. We write Fp for the field with p elements. In 1926, Chebotarëv proved the following theorem (see [3]): Theorem. For any sets I, J ⊆ Fp with equal cardinality, the matrix (ω )i∈I,j...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Mathematicae Silesianae
سال: 2017
ISSN: 0860-2107
DOI: 10.1515/amsil-2016-0013