Linear Algebra (Part 3)

Lectures in this MOOC (36)

Explores symmetric matrices, eigenvalues, and characteristic polynomials in matrix analysis.

Explores the Gram-Schmidt process to obtain orthogonal vectors and bases.

Covers the definition of a scalar product on a real vector space and provides examples.

Explains the step-by-step process of finding the singular value decomposition of a matrix.

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

Explains orthogonal projection onto a subspace and finding orthogonal bases using Gram-Schmidt procedure.

Explores quadratic forms in IR³, matrix properties, diagonalization, and positive definite matrices.

Explores operations with triangular matrices and their role in solving linear systems.

Introduces orthogonal and symmetric matrices in linear algebra with practical examples.

Explains how to solve linear equations using the least squares method to minimize errors in the system.

Covers the singular value decomposition theorem, explaining the construction of orthonormal bases and the matrix representation of the decomposition.

Introduces orthogonal and orthonormal families in vector spaces with scalar products.

Explores symmetric matrices, eigenvalues, eigenvectors, and the spectral theorem in linear algebra.

Explains the Principal Axes Theorem for symmetric matrices and quadratic forms, showing the existence of orthogonal matrices for diagonalization.

Covers the definition of norm, distance between vectors, and Cauchy-Schwarz inequality.

Covers the concept of an orthogonal basis in a vector space.

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