Lectures related to Analytical Study of Space

Explores the analytical study of space, covering relative positions, angles, and properties of lines and planes.

Covers landmarks, coordinate systems, frames, and terminology in coordinates, emphasizing geometric angles and orthogonal vectors.

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

Covers the analytical study of the plan, focusing on points and lines.

Covers the analytical study of space, focusing on points, lines, and planes.

Explores linear dependence and independence of vectors in geometric spaces.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

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

Introduces vector definitions, displacement, addition, and applications in geometry.

Explores parametric equations, vectors, medians, landmarks, and Cartesian equations of lines in the plane.

Covers matrices, linear applications, vector spaces, and bijective functions.

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

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Covers the analytical study of lines in a plane, focusing on equations and geometric interpretations.

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

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Covers the precise description of the relative positioning of objects in space.