I think you can check if two matrices are similar by checking their Jordan canonical forms. If they have the same structure, then the two matrices are similar. To find the Jordan canonical form of a matrix, you
Statement 1: Let A ,B be two square matrices of the same order such that A B=B A ,A^m=O ,n dB^n=O for some positive integers m ,n , then there exists a positi
Key words: Self-similar sets, open set condition, non-negative integral matrices, tilingLet U λ be the union of two unit intervals with gap λ. We show that U λ is a self-similar set satisfying the open set condition if and only if U λ can tile an interval by finitely many of ...
where we introduced the shortcuts cθ≡cosθ and sθ≡sinθ for a generic angle θ, and defined λ345≡λ3+λ4+λ5. The mass matrices for the pseudoscalar and charged components of the two doublets are diagonalized by the angle β: (G0A)=R(β)(a1a2),(G+H+)=R(β)(...
Through vignettes like these, experimental philosophers have repeatedly shown that actions leading to negative consequences are judged as being more intentional than otherwise similar actions leading to positive consequences—often called the Knobe Effect (KE)9,10,11. There is controversy over whether ...
(IBZ). Whereas, D- and E-graphene exhibit only one Dirac point similar to graphene. Therefore, in this work we want to address the key reason behind the occurrence of two Dirac cones in S-graphene. In addition, we are also interested in examining the robustness of the Dirac cones to ...
Correlation matrices are reported in Appendices B and C. The distribution of all variables - with the exception of two-digit number writing accuracy in the English-speaking sample - did not differ substantially from normality. Table 1. Descriptive statistics for each language group. Empty Cell...
Then all the solutions of (1.1) are given by with partitioned as (3.1) and being a projection matrix. The matrices , and satisfy , , , and is a matrix. From now on we restrict . If all solutions of Eqs. (3.2) are commuting, then and . If in (3.2), then , i.e., is a ...
T cell development in the thymus is essential for cellular immunity and depends on the organotypic thymic epithelial microenvironment. In comparison with other organs, the size and cellular composition of the thymus are unusually dynamic, as exemplified
We construct the four-mode squeezed states and study their physical properties. These states describe two linearly-coupled quantum scalar fields, which mak