Lectures related to Signals & Systems I: Preliminary Concepts and Linear Systems

Covers linear applications, matrices, transformations, and the principle of superposition.

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

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

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

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

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

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Covers the basics of linear mapping and coordinate systems.

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

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Explores linear differential equations, including higher-order linear homogeneous equations and equations with constant coefficients.

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

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

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

Explores the exponential of a matrix, properties, Frobenius norm, nilpotent matrices, commutativity, and system solutions.

Explores matrix rank, subspaces, and their role in solving linear systems of equations.

Explores matrix equations, homogeneous systems, solutions, consistency, and properties.