Lectures related to Parametric Resonance: Standard Base

Explores the properties of invertible matrices, including unique solutions and linear independence.

Diagonalization of Matrices: Theory and Examples

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

Diagonalization in 3D Linear Algebra

Explores diagonalization in 3D linear algebra, covering conditions for diagonalizability and eigenvectors.

Matrix Similarity and Diagonalization

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Generalization of Change of Basis Matrices

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Linear Algebra: Matrix Operations

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Matrix Operations: LU Factorization & Linear Independence

Covers LU factorization, linear independence, and matrix equations.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Characteristic Polynomials and Similar Matrices

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

Diagonalizable Matrices: Properties and Examples

Explores the properties and examples of diagonalizable matrices, emphasizing the relationship between eigenvectors and eigenvalues.

Diagonalization: Theory and Examples

Explores diagonalization of matrices through eigenvalues and eigenvectors, emphasizing distinct eigenvalues and their role in the diagonalization process.

Linear Applications and Matrix Calculus

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

Matrix Equivalence Theorems

Explores matrix equivalence theorems for systems of equations and least squares solutions.

Linear Algebra: Applications and Matrices

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

Diagonalization of Matrices

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Optimal Decision Making: The Simplex Method

Introduces the Simplex Method for optimal decision making in linear programming, covering basic and advanced concepts.

Diagonalization of Matrices

Explores the diagonalization of matrices through eigenvectors and eigenvalues.

Matrix Eigenvalues and Eigenvectors

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Linear Algebra: Basis and Matrices

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