Lectures related to Orthogonal Linear Maps

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

Explores orthogonal projection in Euclidean space, emphasizing uniqueness and calculation methods.

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

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

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

Introduces orthogonal families, orthonormal bases, and projections in linear algebra.

Covers the theorems related to orthogonal projection and orthonormal bases.

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

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

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

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

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

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

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

Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.