为了找到该方程组的非平凡解,我们需要满足以下条件: 1) A 的秩(rank)必须大于 b 的维数(或者说 b 不能由 A 的列向量线性表示)。 2) A 的行列式(determinant)不能等于0。 如果满足上述条件,那么该方程组存在非平凡解。 计算结果为:该方程组存在非平凡解。©...
The determinant vanishes, so the system can have a nontrivial solution set. The equations are linearly dependent, as can be seen from the fact that if the first equation is multiplied by 3 and added to the second equation, the result is the same as the third equation. We disregard the ...
). We see that its determinantdet(∂kMλ,k)=1λ{(cothω−ωsinh2ω)2−(ωcoshωsinh2ω−1sinhω)2}=1λsinh4ω(sinh2ω−ω2)(cosh2ω−1)>0, as sinhω>ω and coshω>1 for ω∈(0,∞). Furthermore, the (2,2)-entry of ...
We construct a special plurisubharmonic defining function for a smoothly bounded, strictly pseudoconvex domain in so that the determinant of the complex He... SG Krantz,SY Li - 《Complex Variables Theory & Application An International Journal》 被引量: 10发表: 2000年 On degenerate monge-ampere ...
Answer to: Find one nontrivial solution of Ax = 0, where \displaystyle{ A = \left[ \begin{array}{rr} 3 & 2 \\ 6 & 4 \end{array} ...
In particular there is some interest for confining temperatures, where the holonomy (the asymptotic value of the Polyakov loop) is non-trivial. In the last section I g... PV Baal 被引量: 0发表: 2010年 Fermionic determinant for dyons and instantons with nontrivial holonomy - art. no. ...
The fermionic determinant can be expanded noticing that (55) One can neglect the first term (a constant) and expand the second logarithm to obtain (56) This will yield the effective Lagrangian [90] (57) where \begin{aligned} I_1(m)= & i\int ^\Lambda \frac{d^4p}{(2\pi )^4...
(1.1) is the cohomology class of a flat but topologically non-trivial B-field on. In the following such a B-field will be referred to asfractional. As we will discuss in detail, this background admits an interpretation in terms of two distinct but closely related notions of non-commutative...
The anomalies of a very general class of non local Dirac operators are computed using the ζ-function definition of the fermionic determinant and an asymmetric version of the Wigner transformation. For the axial anomaly all new terms introduced by the non locality can be brought to the standard ...
The determinant formula also enables to calculate the non-degenerate solution of PT-symmetric nonlocal ID-NLSE. Under the continuum limit one can easily recover the degenerate and non-degenerate solutions of PT-symmetric nonlocal NLSE.doi:10.1016/j.physleta.2020.126834Y. Hanif...