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Phase Portrait and Non-linear Systems
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Related lectures (47)
QR Factorization: Least Squares System Resolution
MOOC: Linear Algebra (Part 3)
Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.
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.
Canonical Correlation Analysis: Overview
Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.
Diagonalization of Linear Transformations
Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.
Jordan Normal Form: Theory and Applications
Explores the Jordan normal form and its applications in linear algebra, focusing on diagonalization and cyclic bases.
Subspaces, Spectra, and Projections
Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.
Linear Systems in 2D: Stability
Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.
Eigenvalues and Eigenvectors in 3D
Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.
Singular Value Decomposition
Explores Singular Value Decomposition and its role in unsupervised learning and dimensionality reduction, emphasizing its properties and applications.
Diagonalization in 3D Linear Algebra
Explores diagonalization in 3D linear algebra, covering conditions for diagonalizability and eigenvectors.
Diagonalization of Matrices
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Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.
Characteristic Polynomials and Similar Matrices
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Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.
Singular Value Decomposition (SVD)
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Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.
Diagonalization of Matrices: Theory and Examples
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Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.
Matrix Similarity and Diagonalization
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Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.
Matrix Eigenvalues and Eigenvectors
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Covers matrix eigenvalues, eigenvectors, and their linear independence.
Eigenvalues and Eigenvectors Decomposition
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Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.
Diagonalization of Matrices: Eigenvectors and Eigenvalues
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Covers the concept of diagonalization of matrices through the study of eigenvectors and eigenvalues.
Singular Value Decomposition: Applications and Interpretation
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Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.
Eigenvalues and Eigenvectors: Understanding Matrix Properties
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Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.
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