Unitary matrixThe Birkhoff's theorem states that any doubly stochastic matrix lies inside a convex polytope with the permutation matrices at the corners. We prove that any unitary matrix with equal line sums can also be written as a sum of permutation matrices (with sum of weights equal 1). ...
Intended for first- and second-year graduate courses, the text features examples of group boundaries and key proofs (e.g., of Kovalev's theorem). Annotation ©2010 Book News, Inc., Portland, OR (booknews.com) 展开 DOI: http://dx.doi.org/10.1090/ulect/054 被引量: 60 ...
One can diagonalize the matrix Σ and denote the eigenvalues by di, i = 1, 2, …. Suppose that their sum d = trΣ is finite. Then, Lemmas 2.6 and 2.7 remain valid with β = d/N. Theorem 2.9 Let an infinite-dimensional vector x~N(μ→,Σ) and 0<trΣ<∞.If d1<d/3, n>...
This is related to the fact that the latter necessarily are of infinite range in the orbital basis. Here, we present a theorem tailored to establishing the existence of frustration-free parent Hamiltonians in such a context. We explicitly demonstrate the utility of this theorem in the context ...
For any \( \omega \in \Omega _0 \) such that \( P(\Omega _0) = 1 \), since \( \{{\hat{{\varvec{\theta }}}_k(\omega )\} \) is a bounded sequence by Assumption 2, the Bolzano–Weierstrass Theorem implies that there exists \( \Omega _1 \subset \Omega \) such that ...
A theorem of Sumihiro [13] asserts that all normal toric varieties arise in this way. Toric morphisms between normal toric varieties can likewise be described entirely in terms of their corresponding fans. In particular, a morphism \phi : X_\Sigma \rightarrow X_{\Sigma '} is toric if ...
the fine structure of the spectra1 theory on the s spectrum in dimension five Fueter–Sce–Qian extension theoremHolomorphic functions play a crucial role in operator theory and the Cauchy formula is a very important tool to define ... Fabrizio Colombo · Antonino De Martino · Stefano Pinton ...
On a generalization of a theorem of Baire Sylvester equation for *congruenceWe describe how to find the general solution of the matrix equation AX+~(X*)B=0, where A∈Cm~(×n) and B∈C~(... EG Arin'Sh - 《Uspekhi Mat Nauk》 被引量: 33发表: 1953年 ...
Brouwer was the first one to bring order into the matter. He introduced the terms homotopy, simplicial approximation, and the degree of continuous mapping. Peano’s curves were not bijective and Cantor’s mappings were not continuous. This loophole allowed Brouwer to prove his theorem about the ...
The following theorem of Mañé [289] shows that under natural conditions a compact invariant set has a finite fractal dimension. Let ℒ1 (H, H) be the set of bounded linear operators S′ from H to H which can be split in the following way: S′ = S′1 + S′2 where S′1 is...