Lectures related to Compactness Criterion in Reductive Groups

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

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

Covers the transformation of vectors and tensors in quantum physics.

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Explores indicial notation, vectors, and the transformation law in the context of mass flux density.

Covers rotation matrices and transformations in mathematics, providing examples of rotating vectors in different dimensions.

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

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Explores vector geometry basics, historical perspectives, and practical applications.

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

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

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

Covers the calculation of the cross product in coordinates using vectors in space.

Covers the decomposition of a vector in a base and its applications in speed and distance calculations.

Covers translations, homotheties, and geometric transformations using vectors and matrices.

Explores properties and interpretations of vectors in space, including mixed product and linear dependence.

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

Covers translations, homotheties, and their geometric properties, including reversibility and composition.