Lectures related to Properties of Cross Product: Algebraic Aspects

Symmetric Group and Cycle Decomposition

Explores the Symmetric group, cycle decomposition, Orbit-Stabilizer theorem, and properties of cycles and transpositions.

Symmetric Group and Group Actions

Covers the Symmetric group, cycle decomposition, transpositions, even and odd permutations, and group actions.

Scalar Product: Geometric Properties

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

Multilinear Forms: Alternating and Symmetric

Covers alternating and symmetric multilinear forms in vector spaces over a field.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Permutations and Symmetric Groups

Covers symmetric groups, transpositions, sign of a permutation, and conjugacy classes in permutations.

Determinants: Special Linear Groups and Matrix Properties

Explores the special linear group, matrix properties, and determinant theorems.

Permutations and Signature

Explores permutations, signature, and alternating multilinear forms in vectors.

Algebraic Manipulations: Indices and Tensors in Continuum Mechanics

Provides an overview of algebraic manipulations involving indices and tensors in continuum mechanics.

Symmetric Group and Alternating Group

Explores the Symmetric group, cycle notation, multiplication, the sign of a permutation, and the Alternating group.

Eigenvalues of Coxeter Elements

Explores eigenvalues of Coxeter elements, cyclic permutations, invariance, and decomposition of eigenspaces.

Vector Product: Family of Vectors Orientation

Explains conventions for vector orientation and rules of the right-hand.

Analytical Geometry: Cross Product and Orientation

Explains the cross product in analytical geometry and vector orientation.

Enumeration: Counting Subsets

Covers the concept of enumeration and counting subsets of a finite set with examples and factorial notation.

Tensor Operations: Dot and Cross Products

Covers tensor operations, focusing on dot and cross products and their geometric interpretation.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Vector Algebra: Scalar Product

Explores the scalar product of vectors, including properties and calculation methods.

Indicial Notation and Tensor Components

Covers the manipulation of indicial notation and tensor components, focusing on concepts such as indical notation, free indices, contraction, and the dot product.

Vector Geometry: Basics and Applications

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

Linear Algebra: Sets and Subsets

Explores sets and subsets in linear algebra, emphasizing counting elements and subsets.