Lectures related to From Lattice Products to Tarski's Fixedpoint Theorem

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

Linear Algebra: Linear Dependence and Independence

Explores linear dependence and independence of vectors in geometric spaces.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Elements of Lie Groups and Algebras

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

Analytical Study of Space

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

Vector Transformation and Tense

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

Indicial Notation and Vectors

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

Canonical Analysis: Quadratic Geometry

Explores canonical analysis of quadratic functions to identify conic shapes in planes.

Vector Calculus: Scalars and Vectors

Introduces scalars and vectors, explaining their properties and mathematical operations.

Advanced Physics I: Definitions and Motion

Covers advanced physics topics such as definitions, rectilinear motion, vectors, and motion in three dimensions.

Vectors: Definitions and Operations

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

Decomposition of a Vector

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

Linear Equations: Vectors and Matrices

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

Vectors: Coordinate Calculations

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

Translations and Homotheties

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

Analytical Geometry: Vectors and Operations

Covers the fundamentals of analytical geometry, focusing on vectors and their operations.

Vectors: Fundamentals

Covers the basic concepts related to vectors, including their definition, operations, and properties, as well as applications through examples and the Varignon's theorem.

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Linear Applications: Matrices and Transformations

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

Vector Geometry: Basics and Applications

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