MATH-111(f): Linear Algebra

Lectures in this course (62)

Explores the associated matrix of a linear map, basis formation, and space relationships.

Explores the rank theorem, matrix dimensions, and subspaces, illustrating their relationships and implications.

Explores matrices for linear applications, injective and surjective maps, and base transformations.

Explores linear applications, matrices, ranks, kernels, and dimensions in linear algebra.

Explores changing the base of linear applications and calculating vector images in different bases, emphasizing the use of canonical basis.

Covers the concept of change of basis matrix and its calculation through examples.

Explains the characteristic polynomial, eigenvalues, and VAPs of matrices.

Explores eigenvalues, eigenvectors, characteristic polynomials, and eigenspace in linear applications.

Explores diagonalization conditions, bases by eigenvectors, and generalization of concepts.

Explores diagonalizing matrices, similarity, eigenvectors, and proper spaces.

Explores eigenvalues, determinants, traces, and stochastic matrices in discrete dynamical systems.

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

Explores the concept of orthogonal complement in vector subspaces and fundamental matrix subspaces.

Explores norm, dot product, and orthogonality in vector spaces, including properties and inequalities.

Explores the uniqueness and properties of orthogonal projection, including decomposition, associated matrix, linearity, and practical examples.

Explores the properties and applications of orthogonal matrices in linear algebra, focusing on orthogonality and projections.

Explores QR factorization and the least squares method for solving systems of equations.

Introduces the Gram-Schmidt orthogonalization process to find orthogonal bases for vector subspaces.

Covers least squares, QR factorization, linear models, and regression analysis with applications to experimental data.

Explains the method of least squares and normal equations for finding optimal solutions.

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