MATH-111(e): Linear Algebra

Lectures in this course (158)

Explores linear applications, matrix-vector products, and the linearity of transformations.

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Covers norm, scalar product, and perpendicularity in R^n, including the theorem of Pythagoras and orthogonal complements.

Covers the Gram-Schmidt algorithm for orthonormal bases in vector spaces.

Covers the Gram-Schmidt process, QR decomposition, orthogonal projection theorem, and matrix formulas.

Explains the method of least squares in linear regression to find the best-fitting line to a set of data points.

Covers the diagonalization of symmetric matrices and the spectral theorem.

Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.

Covers the Singular Value Decomposition (SVD) of a matrix and its applications.

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

Focuses on transforming linear systems into triangular matrices to simplify the process of finding solutions.

Explores linear transformations, matrices as functions, and geometric interpretations.

Explores the fundamentals of Singular Value Decomposition, including orthonormal bases and practical applications.

Explores linear regression through least squares and normal equations, emphasizing the importance of minimizing errors for accurate predictions.

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Covers the concept of interesting subspaces related to matrices and the change of basis matrix.

Explores eigenvalues and eigenvectors in matrices through examples and calculations.

Covers linear applications, matrices, injectivity, surjectivity, and matrix multiplication properties.

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