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1 day ago · Special unitary group. In mathematics, the special unitary group of degree n, denoted SU (n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the more general unitary group may have complex determinants with absolute value 1, rather than real 1 in the special case. The group operation is matrix multiplication.
5 days ago · Hence, quaternion matrices, particularly their low-rank approximation models, have been extensively utilized for color image processing tasks recently. For instance, quaternion matrix rank minimization methods [13, 15, 20, 35] and quaternion matrix factorization methods [3, 22]. These methods have achieved remarkable results in tasks such as ...
5 days ago · Furthermore, it is valid for real-valued neural networks and some hypercomplex-valued neural networks such as complex-, quaternion-, tessarine-, and Clifford-valued neural networks. However, hypercomplex-valued neural networks are a type of vector-valued neural network defined on an algebra with additional algebraic or geometric properties.
4 days ago · Dear all, I have created an ellipsoid with its shape (1,1,6) as shown. I would like to make its tip to point to the direction (x,y,z). I was wondering how to define quatw, i, j, k. I try to figure out how quaternion work but still in confusion. I cannot find the expression of quaternion in LAMMPS manual also. Thank you,
5 days ago · I am testing a SW tool against a formula and I have noticed that sometimes the signs are different. The calculated position of an object in 3D space, from a SW tool, is as follows: Quaternion (-Q0, Qx, Qy, Qz) From a formula, I obtained: (Q0,-Qx, -Qy, -Qz) Reminder: Answers generated by artificial intelligence tools are not allowed on Stack ...
5 days ago · The first quaternion is a phase (see Equation (30) of ); the second is a geometric factor that orients the spin disc in the Body Fixed Frame, BFF; and the last is a field quaternion that sets the field position in the Laboratory Fixed Frame, LFF. Since Q-spin has structure, the BFF and LFF are needed.
5 days ago · The conference was structured around the four main mathematical themes in post-quantum cryptography: lattices, error-correcting codes, systems of non-linear equations and isogenies. This blog post is based on Benjamin Wesolowski’s introductory talk “Foundations of isogeny-based cryptography”, about hardness assumptions behind isogeny ...
