Lectures related to Orthogonal Projections and Reflections in 2D

Diagonalization of Matrices

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Linear Applications and Eigenvectors

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

Characteristic Polynomials and Similar Matrices

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

Projections and Symmetries

Explores projections on lines and symmetries in 2D space, emphasizing fixed points and symmetric matrices.

Subspaces, Spectra, and Projections

Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Symmetric Matrices: Diagonalization

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Spectral Decomposition of Symmetric Matrices

Explores the spectral decomposition of symmetric matrices, including diagonalization and orthogonal basis change matrices.

Linear Algebra: Singular Value Decomposition

Delves into singular value decomposition and its applications in linear algebra.

Symmetric Matrices: Properties and Decomposition

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Orthogonal Matrices & Spectral Decomposition

Covers the process of finding orthogonal bases and spectral decomposition of symmetric matrices.

Symmetric Matrices and Eigenvectors

Covers the concept of symmetric matrices, orthogonal bases, and eigenvectors.

Diagonalization of Symmetric Matrices

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Diagonalization of Linear Transformations

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Diagonalization in Symmetric Matrices

Explores diagonalization in symmetric matrices, emphasizing orthogonality and orthonormal bases.

Projections and Applications

Explores projections in R³, matrix properties, and trace concepts with practical examples.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Eigenvalues and Eigenvectors: Understanding Matrix Properties

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Translations and Homotheties

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.