Lectures related to Gauss Representation

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Linear Algebra: Abstract Concepts

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Matrix Operations and Vector Spaces

Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.

Vector Spaces: Operations and Linear Transformations

Explores vector space operations, linear transformations, matrix representation, and linear applications.

Matrix Equations: Linear Combinations

Covers matrix equations as linear combinations, vector spaces, and geometric interpretations.

Complex Numbers: Applications and Representations

Explores the origin, applications, and representations of complex numbers in crystallography and materials science, including their graphical, polar, and exponential forms.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Linear Algebra: Matrices and Linear Applications

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

Projection Matrix

Demonstrates the proof of a matrix as a projection matrix in Rn.

Finding a Base from a System of Generators

Covers the process of finding a base from a system of generators in linear algebra.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Vector Spaces: Definitions and Properties

Covers the definitions and properties of vector spaces, including axioms and examples.

Linear Algebra Basics

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Signal Representations

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Linear Algebra: Basis and Matrices

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Differential of a Morphism

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.

Vector Spaces: Properties and Examples

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

Linear Algebra Review: Vector Spaces and Matrix Operations

Offers a quick review of key linear algebra concepts essential for further topics.

Orthogonal Families and Projections

Introduces orthogonal families, orthonormal bases, and projections in linear algebra.

Linear Equations and Vector Spaces

Delves into linear equations, vector spaces, and matrix operations, exploring solutions and representations through examples and algebraic methods.