Eigenvalues and Eigenvectors

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Related lectures (50)

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Diagonalization of Linear Transformations

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

Linear Algebra: Canonical Basis

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.

Calcul de valeurs propres

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.

Subspaces, Spectra, and Projections

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

Eigenvalues and Optimization: Numerical Analysis Techniques

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Singular Values: Definitions and Properties MOOC: Linear Algebra (Part 3)

Covers the concept of singular values in linear algebra and their properties, including diagonalization and practical examples.

Linear Systems in 2D: Stability

Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.

Effect of Rounding Errors in Linear Systems Log in to Mediaspace to watch this video

Explores the effect of rounding errors in solving linear systems using the LU factorization method.

Eigenvalues and Eigenvectors Decomposition Log in to Mediaspace to watch this video

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Numerical Analysis: Linear Systems Log in to Mediaspace to watch this video

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

Characteristic Polynomials and Similar Matrices Log in to Mediaspace to watch this video

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

Diagonalization of Matrices Log in to Mediaspace to watch this video

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

Matrix Eigenvalues and Eigenvectors Log in to Mediaspace to watch this video

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Diagonalization of Matrices: Theory and Examples Log in to Mediaspace to watch this video

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

Singular Value Decomposition (SVD)Log in to Mediaspace to watch this video

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

Matrix Diagonalization: Spectral Theorem Log in to Mediaspace to watch this video

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

Eigenvalues and Fibonacci Sequence Log in to Mediaspace to watch this video

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

Eigenvalues and Eigenvectors: Understanding Matrix Properties Log in to Mediaspace to watch this video

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

Iterative Methods: Linear Systems Log in to Mediaspace to watch this video

Explores iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods, Cholesky factorization, and preconditioned conjugate gradient.

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