The paper studies algebraic strong shift equivalence of matrices over $n$-variable polynomial rings over a principal ideal domain $D$($n\\leq 2$). It is proved that in the case $n=1$, every non-zero matrix over $D[x]$ has a full rank factorization and every non-nilpotent matrix ...
来源期刊 Communications 1972/01/01 研究点推荐 T-Matrices For (C, r) 0关于我们 百度学术集成海量学术资源,融合人工智能、深度学习、大数据分析等技术,为科研工作者提供全面快捷的学术服务。在这里我们保持学习的态度,不忘初心,砥砺前行。了解更多>>
On matrix equivalence and matrix equationsRoth's theorem on the solvability of matrix equations of the form AX YB= C is proved for matrices with coefficients from a division ring or a ring which is module-finite over its center.doi:10.1016/0024-3795(79)90044-2William H. Gustafson...
Let Sn be the set of all n x n permutation matrices and let X, Y ∈ Sn. An equivalence relation is defined as follows: X Y if and only if X can be obtained from Y by a sequential moving of the first row or column to the last place. The cardinal number of the factor-set Sn/...
(1986). On the equivalence of µ-invariant measures for the minimal process and its q-matrix. Stochastic Process. Appl. 22, 203-221.P. K. Pollett. On the equivalence of µ-invariant measures for the minimal process and its q-matrix. Stochastic Process. Appl., 22(2):203-221, 1986...
of the system’s dynamics34. This equivalence implies that the superior efficacy of geometric eigenmodes in the reconstruction of diverse patterns of brain activity results from a fundamental role of wave dynamics in shaping these patterns, as predicted by NFT. This prediction has been confirmed thr...
Image texture, the relative spatial arrangement of intensity values in an image, encodes valuable information about the scene. As it stands, much of this potential information remains untapped. Understanding how to decipher textural details would afford
We establish the equivalence of both problems when the number of sources is assumed to be unknown and can potentially exceed the number of sensors. Additionally, it is shown that when the source waveforms satisfy certain orthogonality conditions, the Toeplitz-constrained maximum-likelihood covariance ...
In order to improve k-anonymity, l-diversity [5] and t-closeness [15] are proposed to guarantee that equivalence classes have diverse sensitive values, but they are still vulnerable to similarity attacks. Traditional generalization methods are highly dependent upon spatial locality [31], and thus...
For example, if d>1 and A is a d×d matrix over a finite field, then it cannot be the case that both AA∗ and A∗A are nilpotent matrices with a single Jordan block. In order to state the result, we need to introduce some notation. Let α be a partition of m and β a ...