Lectures related to Change of Base in Linear Applications

Linear Algebra in 3D: Determinants and Inverses

Explores determinants in 3D space and their role in linear algebra.

Covers matrix rank, determinant, and decomposition in linear algebra.

Linear Algebra: Change of Basis Matrices

Explores change of basis matrices in linear algebra, emphasizing the importance of understanding matrix transformations between different bases.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Linear Applications and Matrices

Delves into the bijection between linear applications and matrices, exploring linearity, injectivity, surjectivity, and the consequences of this relationship.

Base Change Matrix: Transition and Equivalence in Matrices

Covers the base change matrix, transition matrix, and equivalence of matrices in linear algebra.

Linear Algebra: Organization and Exercises

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

Eigenvalues and Eigenvectors in 3D

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Diagonalization Criteria

Covers the second criterion of diagonalization and similar matrices in linear applications.

Linear Algebra: Applications and Matrices

Explores linear algebra concepts through examples and theorems, focusing on matrices and their operations.

Vector Spaces: Properties and Operations

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

Linear Algebra: Multilinear Groin and Determinants

Explores multilinear groin and determinants, including the Sarrus rule and proof by induction.

Operations on Linear Applications

Covers operations on linear applications in R³, including definitions, behavior of compositions, and determinants.

Linear Algebra: Basis and Matrices

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

Linear Applications and Matrix Calculus

Explores linear applications, matrices, injectivity, unique solutions, and matrix operations.

Linear Algebra: Rank Theorem

Explores the Rank Theorem in linear algebra, covering matrix properties and determinants.

Linear Algebra: Applications and Bases

Explores unique solutions, linear dependence, canonical bases, and linear maps in linear algebra.

Matrix Representations of Linear Applications

Covers the matrix representations of linear applications and the equivalence between matrices.

Linear Algebra Fundamentals

Explores linear algebra fundamentals, including key definitions, theorems, and practical applications in mathematics and technology.

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.