Concept

Quaternion

Related lectures (17)

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

Proof of Lagrange Theorem

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

Fermat's Theorem: Sums of Squares

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

Quadratic Spaces and Quaternion Algebra

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

Quaternion Algebra: Properties and Applications

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

Conductor of X: Waldsparger Formula and Subconvexity Bound

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

Fourier Expansion and Quaternion Algebra

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

Quaternion Algebra and Hermite Space

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

Abelianization of Fundamental Group

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

Division Rings and Ideals

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

Linear Projective Groups

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

Flat Space-Time: Conditions and Theorems

Covers the necessary conditions and theorems to have flat space-time and discusses the symmetry properties of the Riemann tensor.

Group Homomorphisms

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

Manopt: Optimization Toolbox for Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Complex Numbers: Introduction and Operations

Introduces complex numbers and their forms, including Cartesian, polar, and exponential forms, and explains how to find the argument of a complex number.

Direct Geometric Modeling: Kinematics

Explores Direct Geometric Modeling in kinematics, focusing on operational coordinates and orientation using joint variables and quaternions.

Rotation in Two Dimensions

Explores rotation in two dimensions, analyzing moment of inertia, acceleration, and stability using practical examples.