We determine the local symmetries and transformation properties of translationally invariant matrix product states (MPS). focus on physical dimension $d=2$ bond $D=3$ use procedure introduced in D. Sauerwein et al., Phys. Rev. Lett. 123, 170504 (2019) to all (including non--global) those states. identify classify stochastic transformations (SLOCC) that are allowed among MPS. scrutinize two very...

Abstract In this paper we generalize the space $\hat{\ell }_{k}$ ℓ ˆ k of absolutely almost convergent series (J. Math. Anal. Appl. 161:50–56, 1991) via weighted mean transformations. We study some inclusion relations and their ...

A QR–method for computing the singular values via semiseparable matrices. Abstract The standard procedure to compute the singular value decomposition of a dense matrix, first reduces it into a bidiagonal one by means of orthogonal transformations. Once the bidiagonal matrix has been computed, the QR–method is applied to reduce the latter matrix into a diagonal one. In this paper we propose a ne...

8 Elementary operations and the rank of a matrix 25 8.1 Gauss transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 8.2 Elementary row operations . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.3 The augmented matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.4 Row reducing a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 8.5 Elem...

Abstract A new type of supersymmetric transformations of the coupled-channel radial Schrödinger equation is introduced, which do not conserve the vanishing behavior of solutions at the origin. Contrary to usual transformations, these “non-conservative” transformations allow, in the presence of thresholds, the construction of potentials with coupled scattering matrices from uncoupled potentials....

The relations between evaluation of Ore polynomials and pseudo-linear transformations are studied. The behavior of these transformations under homomorphisms of Ore extensions, in particular with respect to algebraicity, is analyzed leading to characterization of left and right primitivity of an Ore extension. Necessary and sufficient conditions are given for algebraic pseudo-linear transformati...

Parikh matrices have been extensively investigated due to their usefulness in studying subword occurrences in words. Due to the dependency of Parikh matrices on the ordering of the alphabet, strong M-equivalence was proposed as an order-independent alternative to M-equivalence in studying words possessing the same Parikh matrix. This paper introduces and studies the notions of strong (2 · t) an...

In this paper, I will explore basic properties of the group PSL(2,R). These include the relationship between isometries of H2, Möbius transformations, and matrix multiplication. In addition, this paper will explain a method of characterizing the aforementioned transformations by the trace of their matrices through looking at the number of xed points of a transformation.

The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota–Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.