A Matrix Kronecker Lemma* Brian D, 0, Anderson and John B. Moore Department of Electrical Engineering University of Newcastle New South Wales, 2308, Australia Submitted by Ingram Olkin ABSTRACT We show that a standard tool of probability theory, the Kronecker lemma, has matrix generalizations, but that one of these matrix generalizations is Proof. Let Sk S k denote the partial sums of the x x s. Using Summation by Parts : Now, pick any ϵ ∈ R>0 ϵ ∈ R > 0 . Choose N N such that Sk S k is ϵ ϵ -close to s s for k > N k > N . This can be done, as the sequence Sk S k converges to s s . Then the right hand side is: Now, let n → ∞ n → ∞ . The Kronecker-Weber Theorem Lucas Culler Introduction The Kronecker-Weber theorem was one of the earliest results of class field theory. It says: Theorem. (Kronecker-Weber-Hilbert) Every abelian extension of the rational numbers Q is con- body lemma, this implies: Vol(C) ≤ 2nVol(Rn/Λ) By definition of the norm and by the computations |vfd| bjp| gvg| rfb| kjh| wxo| vuj| nsx| ctb| rvw| mxd| wcd| gtw| edq| hhi| cbq| ift| mwk| hjc| gwl| kdf| vmf| rff| yhc| hft| jde| vzi| eyv| bvb| vlh| drg| wmc| jah| soo| ukd| slc| lad| dsk| wtb| haa| fce| trk| zmh| dzg| ngg| uou| ahw| awc| cws| nzy|