Fourier Expansion and Quaternion Algebra

Related lectures (13)

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

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.

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.

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

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

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