Lecture

Quaternion Algebra: Properties and Applications

Related lectures (31)

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.

Covers weak solutions in the finite element method, emphasizing continuity and the Cauchy-Schwarz inequality.

Explores Markov chains, transition matrices, distribution, and random walks.

Explores the regulation of therapeutic products, covering legal requirements, product classification, market access, and advertising rules.

Explains the use of operators for transferring data between activities in an orchestration graph.

Explores continuous random variables and their properties, including support and cumulative distribution functions.

Covers the binary choice model, error term assumptions, specific constants, invariances, and distribution properties.

Explores the benefits of deeper networks in deep learning and the importance of over-parameterization and generalization.

Delves into the binary choice model, error term specification, and Extreme Value distribution properties.

Explores linear projective groups, quaternions, subgroup generation, and normality.

Explores the evolution of the distribution function describing particles in phase space.