Concept

Split-quaternion

Related lectures (23)

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

Covers the properties and applications of quaternion algebra, including norm calculations and distribution in different spaces.

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

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

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

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

Explores quadratic surfaces in 3D space, discussing hyperboloids and their Cartesian equations, emphasizing the importance of reference frames.

Explores abelianization examples, homomorphisms, and isomorphisms in group theory.

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

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

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

Covers division rings, fields, and ideals in commutative rings with examples in Z and quaternions.

Explores geometric surfaces, rules between shapes, and architectural applications.

Explores Cramer's Rule for solving linear equations and calculating matrix inverses.

Explores the theory and applications of matrix determinants, emphasizing their role in matrix invertibility and solution uniqueness.

Showcases the Wacom Bamboo Folio for real-time writing and sharing with Zoom.

Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Explores surfaces with constant curvature, rules between geometric elements, and the generation of sections in geometry.

Explores surfaces, curvature, ruled surfaces, and practical applications in geometry.