Linear Algebra: Decomposition Theorems

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Explores eigenvalues, eigenvectors, and methods for solving linear systems with a focus on rounding errors and preconditioning matrices.

Eigenvalues and Eigenvectors: Understanding Matrix Properties

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

Diagonalization of Linear Transformations

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Singular Value Decomposition (SVD)

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

Diagonalization of Symmetric Matrices

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Diagonalization of Linear Maps

Explores the diagonalization of linear maps by finding a basis formed by eigenvectors.

Diagonalization of Matrices and Least Squares

Explores diagonalization of matrices, similarity relations, and eigenvectors in linear algebra.

Eigenvalues and Fibonacci Sequence

Covers eigenvalues, eigenvectors, and the Fibonacci sequence, exploring their mathematical properties and practical applications.

Linear Regression: Absence or Presence of Covariates

Explores linear regression with and without covariates, covering models captured by independent distributions and tools like subspaces and orthogonal projections.

Singular Value Decomposition: Example

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