Quadratic Spaces and Quaternion Algebra

Related lectures (28)

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

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Covers linear applications, matrices, transformations, and the principle of superposition.

Explores Lie groups, scalar fields, and vector spaces transformations.

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

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

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