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 ...
K. HEDRICK, On equivalence of quadratic loss functions, Internat. J. Control, 11 (1970), pp. 213-222.Kreindler, E. and Hedrick, 1. K., "On equivalence of quadratic loss functions," Int. l. Cant., 11,213 (1970).Kreindler, E., and J. Hedrick, "On the Equivalence of Quad- rat...
K. (1986). On the equivalence of µ-invariant measures for the minimal process and its q-matrix. Stoch. Process. Appl. 22, 203-221.Pollett P K. On the equivalence of μ-invariant measures for the minimal process and its q-matrix. Stochastic Process Appl, 1986, 22: 203-221...
J.W. Hilgers, On the equivalence of regularization and certain reproducing kernel Hilbert space approaches for solving first kind problems. SIAM J. Numer. Anal. 13, 172–184 (1976) Article MathSciNet MATH Google Scholar E. Hille, Introduction to general theory of reproducing kernels. Rocky ...
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...
Primitive equivalence of graphs and matrices was used by Enomoto, Fujii and Watatani to classify Cuntz-Krieger algebras of 3x3 irreducible matrices. In this paper it is shown that the definition of primitive equivalence can be simplified using primitive transfers of matrices that involve only two ...
Integral systems (1.1) arise in the theory of diffusion processes with two measures [35,38]. In the theory of stochastic processes the Eq. (1.3) describes generalized diffusion processes which includes both diffusion processes and birth and death processes [18,19,23,31]. The system (1.1) is...
On the Equivalence of Nonnegative Matrix Factorization and K-means — Spectral Clustering Chris Ding Xiaofeng He Horst D. Simon Rong Jin December 4, 2005 Abstract We provide a systematic analysis of nonnegative matrix factorization (NMF) relating to data cluster- ing. We generalize the usual X ...
Structure of tridiagonal matrices, where “” denotes nonzero entries Full size image Our Results.We improve theW[1]-hardness ofDeterminant Maximizationdue to Koutis [27] by showing that it is stillW[1]-hard even if an input matrix is extremely sparse or low rank, or an approximate soluti...
(2008c). On the equivalence of Cohen’s kappa and the Hubert-Arabie adjusted Rand index. Journal of Classification, 25(2), 177–183. Article MathSciNet MATH Google Scholar Warrens, M.J. (2008d). On the indeterminacy of resemblance measures for binary (presence/absence) data. Journal of...