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Clustering of Image Covariance Matrixes on Lie Group Manifold
AbstractAn image clustering method based on covariance matrix and mean-shift algorithm on Lie group manifold is proposed. Firstly, according to the...
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Algebra
Algebra is the branch of mathematics that uses letters in the place of numbers, where the letters stand for variables or constants that are used in...
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On Some Lie Groups in Degenerate Geometric Algebras
In this paper, we introduce and study several Lie groups in degenerate (Clifford) geometric algebras. These Lie groups preserve the even and odd...
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Lie Group and Lie Algebra
In the last lecture, we introduced the description of rigid body motion in the three-dimensional world, including the rotation matrix, rotation...
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Geometric Algebra and Distance Matrices
We present a new approach to the problem of recognizing an Euclidean distance matrix, based on Conformal Geometric Algebra. Such matrices are...
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Geodesic Flows of \(\alpha \) -connections for Statistical Transformation Models on a Compact Lie Group
The geodesic flows of the \(\alpha \)...
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Lie group manifold analysis: an unsupervised domain adaptation approach for image classification
Domain adaptation aims to minimize the mismatch between the source domain in which models are trained and the target domain to which those models are...
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Large Language Model for Geometric Algebra: A Preliminary Attempt
Geometric algebra serves as the unified language of mathematics, physics, and engineering in the 21st century. Coinciding with the era of artificial...
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Geometric algebra-based multiscale encoder-decoder networks for 3D motion prediction
3D human motion prediction is one of the essential and challenging problems in computer vision, which has attracted extensive research attention in...
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Algebra
Computable algebra forms a core area of research in modern computability theory. It has a long history, stretching back to the first half of the 20th...
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On Implementation of Numerical Methods for Solving Ordinary Differential Equations in Computer Algebra Systems
AbstractThis paper presents an original package for investigating numerical solutions of ordinary differential equations, which is built in the Sage...
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A Cyclic Proof System for Guarded Kleene Algebra with Tests
Guarded Kleene Algebra with Tests ( \(\texttt{GKAT}\)...
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Geometric Algebra
This can only be a brief introduction to geometric algebra as the subject really demands an entire book.
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Lie Group Quaternion Attitude-Reconstruction of Quadrotor UAV
The quadrotor unmanned aerial vehicles (UAVs) have already gained enormous popularity, both for commercial and hobby applications. They are utilized...
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Variational Integrators for Stochastic Hamiltonian Systems on Lie Groups
Motivated by recent advances in stochastic geometric modelling in fluid dynamics, we derive a variational integrator for stochastic Hamiltonian...
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Properties of Morphological Dilation in Max-Plus and Plus-Prod Algebra in Connection with the Fourier Transformation
The basic filters in mathematical morphology are dilation and erosion. They are defined by a structuring element that is usually shifted pixel-wise...
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Geometry-Preserving Lie Group Integrators for Differential Equations on the Manifold of Symmetric Positive Definite Matrices
In many applications, one encounters time series that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are...
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On the Complexity of Linear Algebra Operations over Algebraic Extension Fields
In this paper, we study the complexity of performing some linear algebra operations such as Gaussian elimination and minimal polynomial computation...