Quaternion Algebra: Properties and Applications

Related lectures (31)

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Covers 3D rotations, quaternions, and matrices of direction cosines, providing an elegant solution to the limitations of rotation matrices.

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Explores quadratic spaces, norms, and quaternion algebra over fields.

Discusses Fourier expansion, quaternion algebra, and Whittaker model in automorphic forms.

Covers the equidistribution of representations of integers by ternary forms and the conductor of X.

Explores diffusion models, focusing on generating samples from a distribution and the importance of denoising in the process.

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Covers the proof of Lagrange Theorem and explores quaternions, prime numbers, and equations.

Explores Fermat's Theorem, factorization of integers, properties of Z[i], and Hurwitz quaternions.

Covers quaternion algebra, Waldspurger formula, and Hermite space in relation to L-functions and inner products.