Advanced Linear Algebra: Matrices Conjugation and Equivalence

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Matrix Representations: Linear Maps

Explores matrix representations of linear maps and their invariance, using examples and special cases.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Linear Algebra: Matrices and Endomorphisms

Explores properties of matrices, endomorphisms, and linear applications in vector spaces.

Linear Algebra: Organization and Exercises

Covers the organization of linear algebra course and exercises for civil engineering and environmental sciences students.

Tensor Products and Symmetric Power

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Geometric Transformations in R2 and R3

Explores geometric transformations in R2 and R3, including linear transformations, projections, matrices, and trace properties.

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Linear Algebra Basics

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Vector Spaces Equivalence

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.