Theorem 2.11: Every linearly independent list ofvectorsin a finite-dimensional vector space can be extended to a basis of the vector space 这两条实际上说了,可以张成向量空间的一组向量看起来比一组基“大”,而一组线性无关的向量看起来比一组基“小”。 并且,上次我们用到了一个“计算机算法”式的...
. General Topology and Its Relations to Modern Analysis and Algebra, IV, Part B: Contributed Papers, Society of Czechoslovak Mathematicians and Physicists, Prague (1977). pp, 357–360. Google Scholar U. Prat, “On a weak sum theorem in dimension theory,” Isr, J. Math.,19, No. 3, ...
A fairly complete theorem is proved relating to conditions under which strong or weak convergence will hold for an estimate of the McMillan degree when the estimation is based on minimisation of a criterion of the form log det (惟 n) + nC(T)/T, where 惟 n, is the estimate of the ...
Caratheodory's theorem says that the minimum occurs already with N at most one plus the dimension of B(Y, X) as a vector space over the reals; that is, N≤ n2 + 1 in the case of real scalars and N≤ 2n2 + 1 when the scalars are complex. (By being slightly more careful ...
The Severi and Scorza varieties are the limiting cases of a theorem of Zak conjectured by Hartshorne. Zak also classified the Severi and Scorza varieties. ... V Popov - Springer 被引量: 21发表: 2004年 On the exceptional series, and its descendants Many of the striking similarities which occ...
Theorem 1 The category of quasinormal toric supervarieties with one odd dimension is equivalent to the category of decorated fans.7 The Geometry of Quasinormal Toric Supervarieties Now that we have described the category of quasinormal toric supervarieties of one odd dimension, we seek to understand...
A generalization of Grothendieck's non-vanishing theorem is proved for a module which is finite over a local homomorphism. It is also proved that the Goren... L Khatami,M Tousi,S Yassemi 被引量: 1发表: 2006年 TEST MODULES, WEAKLY REGULAR HOMOMORPHISMS AND COMPLETE INTERSECTION DIMENSION We...
9. Theorem.(Principal Ideal Theorem) Let A be a Noetherian ring, f_1 ,\dotsb ,f_n\in A , then the minimal prime ideal containing (f_1, \dotsb ,f_n ) has height \leq n . As a Corollary, we have 10. Corollary. Let A be a Noetherian ring and if f is neither a zero-divi...
However, the theorem of Medina and Revoy also provides us with the tools to circumvent this conclusion. We find that the double extension structure can be used as a bootstrap to construct out of any kinematical algebra without invariant metric a new extended algebra that has one by construction...
As is well known, the duality mapping on classical linear systems, which is defined by a mere transposition of matrices, makes the concepts of controllability and observability dual to each other. This classical duality theorem, due to Kalman, is extended to a certain important class of multidime...