Lectures related to Quadratic Best Approximation

Orthogonality and Least Squares Method

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Orthogonality and Least Squares Method

Introduces orthogonal vectors, scalar product, Euclidean norm, Pythagorean theorem, and unit vectors.

Orthogonal Projection: Euclidean Space

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

Orthogonality and Scalar Product

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Scalar Product and Euclidean Spaces

Covers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.

Orthogonality and Least Squares Methods

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

Orthogonality and Least Squares Method

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

Matrices and Orthogonal Transformations

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

Orthogonality and Subspaces

Explores orthogonality, vector norms, and subspaces in Euclidean space, including determining orthogonal complements and properties of subspaces and matrices.

Vector Spaces: Properties and Examples

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

Vector Calculus in 3D

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.

Orthogonal Bases, Orthonormal/Orthonormalized Bases

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

Orthogonal Projection on Vector Subspace

Explains orthogonal projection on a vector subspace in Euclidean space.

Orthogonality and Least Squares

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Linear Algebra: Normal Equations and Symmetric Matrices

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

Orthogonal Vectors and Projections

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Orthonormal Vectors Properties

Explores the properties of orthonormal vectors in Euclidean space through key equations and demonstrations.

Linear Applications and Eigenvectors

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Diagonalization of Matrices and Least Squares

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

Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.