Linear Algebra (Part 3)

Lectures in this MOOC (36)

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

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Explains orthogonal projection on a vector subspace in Euclidean space.

Covers the concept of singular values in linear algebra and their properties, including diagonalization and practical examples.

Explores changing bases for rotations, orthogonal planes, and vector transformations under rotation.

Explores the fundamental theorem on singular values and the formation of orthonormal bases from eigenvectors.

Explains the QR factorization theorem and demonstrates the Gram-Schmidt procedure with an example.

Covers the QR factorization of a matrix A into Q and R.

Explores orthogonal base change in linear algebra, focusing on matrices and transformations.

Explores the Gram-Schmidt process for constructing orthogonal vectors in a vector space.

Explores orthogonality, triangle inequality, and the Pythagorean theorem in vector spaces.

Explores approximating functions with polynomials in inner product spaces, focusing on degree 2 and cosine functions.

Covers the properties of symmetric matrices, orthogonal matrices, and eigenvalues.

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

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Explores the equivalence conditions for orthogonal matrices and includes examples of rotations.

Covers finding the best quadratic approximation for a given function in a continuous space.

Covers the method of diagonalizing a symmetric matrix using an orthogonal matrix.

Introduces the first step in finding an orthogonal/orthonormal base in a vector space.

Explores the best quadratic approximation in Euclidean spaces, emphasizing least squares.

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