Lectures related to Quaternion Algebra and Hermite Space

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.

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Orthogonality and Gram-Schmidt Process

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.

Magnetic Induction

Explains magnetic induction, force on a dipole, torque, and applications in macroscopic systems.

Wave Equation: Euler-Paissan-Doubana

Covers the wave equation and introduces the Euler-Paissan-Doubana formula, emphasizing key concepts.

Studying Mechanics: Vector Calculus

Covers vector calculus, including scalar and vector products, with insights from Dr. Sylvain Bréchet.

Scalar Product and Vectors

Introduces vector components, scalar and vector products, and their properties, including colinear and coplanar vectors, and the rule of the right hand.

Scalar Product: Geometric Properties

Covers the definition and properties of the scalar product, including geometric interpretations and algebraic properties.

Group Homomorphisms

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