Results 41 to 50 of about 240,116 (294)
Quad-Quaternion MUSIC for DOA Estimation Using Electromagnetic Vector Sensors
EURASIP Journal on Advances in Signal Processing, 2008 A new quad-quaternion model is herein established for an electromagnetic vector-sensor array, under which a multidimensional algebra-based direction-of-arrival (DOA) estimation algorithm, termed as quad-quaternion MUSIC (QQ-MUSIC), is proposed.
Xiaofeng Gong, Zhiwen Liu, Yougen Xu
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Canonical quaternion algebra of the Whitehead link complement
, 2023 Let ΓM be the fundamental group of a knot or link complement M. The discrete faithful representation of ΓM into PSL2(C) has an associated quaternion algebra. We can extend this notation to other representations, which are encoded by the character variety
Palmer, Rebekah, 0000-0002-1240-6759
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Quaternion Algebras and the Algebraic Legacy of Hamilton's Quaternions
Irish Mathematical Society Bulletin, 2006 We describe the basic definitions and fundamen- tal properties of quaternion algebras over fields and proceed to give an account of how Hamilton's 1843 discovery of the quaternions was a major turning point in the subject of al- gebra. Noncommutative algebra started here! We will em- phasize especially the theory of division algebras and other kinds of
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Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Abstract and Applied Analysis, 2013 General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties
Mawardi Bahri +2 more
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Quaternion based generalization of Chern–Simons theories in arbitrary dimensions
Physics Letters B, 2017 A generalization of Chern–Simons gauge theory is formulated in any dimension and arbitrary gauge group where gauge fields and gauge parameters are differential forms of any degree.
Alessandro D'Adda +3 more
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, 2021 This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature.
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Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application
AxiomsConvolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter ...
Rongbo Wang, Qiang Feng
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Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
Special Matrices, 2014 L. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331(2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformationsA ↦ ˜S−1AS in which S is a nonsingular quaternion matrix ...
Klimchuk Tatiana, Sergeichuk Vladimir V.
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Visualizing Quaternion Multiplication
IEEE Access, 2017 Quaternion rotation is a powerful tool for rotating vectors in 3-D; as a result, it has been used in various engineering fields, such as navigations, robotics, and computer graphics. However, understanding it geometrically remains challenging, because it
Jongchan Baek +3 more
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IEEE Access, 2021 For scenarios of coherent underwater sources at low signal-to-noise ratio (SNR), a novel quaternion-based DOA algorithm without eigendecomposition is proposed using a linear vector-hydrophone array.
Yi Lou +3 more
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