MATH-111(c): Linear Algebra

Lectures in this course (59)

Covers the concept of expressing vectors in proper bases and the importance of diagonalization of matrices.

Explores eigenvalues, matrix trace, and similarity, highlighting their significance in matrix properties.

Covers matrix equations, solutions, and transition matrices between bases.

Covers the concept of diagonalizability of matrices and explores eigenvalues and eigenvectors.

Explores the criteria for diagonalizing matrices and their practical applications.

Explains orthogonal families, bases, and projections in vector spaces.

Covers the concept of orthogonal projection and its applications in vector analysis.

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Explains orthogonal matrices, Gram-Schmidt process, and best vector approximation in subspaces.

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.

Covers the factorization of a matrix and the least squares method.

Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

Covers the concept of symmetric matrices, orthogonal bases, and eigenvectors.

Explores spectral and singular value decompositions of matrices.

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Covers the spectral decomposition of matrices and change of basis applications.

Covers bases, transformations, and matrix decompositions in linear algebra.

Explores methods for solving linear systems and building solutions step by step.

Covers linear transformations, change of bases, and diagonalization of matrices.

Page 3 of 3