Vectors and Tensors: Mathematical Preliminaries and Spectral Decomposition

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

Subspaces, Spectra, and Projections

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

Spectral Theorem Recap

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

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Diagonalization in Symmetric Matrices

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

Matrices and Quadratic Forms: Key Concepts in Linear Algebra

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Spectral Theorem: Min-Max Criterion

Explores the Spectral Theorem, emphasizing the Min-Max Criterion for symmetric matrices and the properties of positive definite matrices.

Linear Algebra: Eigenvalues and Eigenvectors

Explores eigenvalues, eigenvectors, diagonalization, and spectral theorem in linear algebra.

Matrices and Networks

Explores the application of matrices and eigendecompositions in networks.