Lectures related to Linear Applications and Eigenvectors

Orthogonal Vectors and Projections

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

Orthogonality and Projection

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

Orthogonal Bases and Projection

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

Diagonalization of Matrices and Least Squares

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

Orthogonality and Least Squares Methods

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

Orthogonality and Least Squares

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

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Vector Calculus in 3D

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

Orthogonal Families and Projections

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

Orthogonality and Subspace Relations

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Matrices and Orthogonal Transformations

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

Orthogonal Families and Projections

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

Singular Value Decomposition: Applications and Interpretation

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

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Linear applications and eigenvalues

Covers the representation of linear applications through matrices, diagonalizable matrices, bases, dot product, orthogonality, and orthogonal vectors.

Orthogonality and Least Squares Method

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

Diagonalization of Matrices

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Orthogonality: Norm, Scalar Product, Perpendicularity

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