Direct Methods for Linear Systems of Equations

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Related lectures (28)

Chaos and Lyapunov Exponents: Analyzing Predictability

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Matrix Factorization: LU Decomposition

Explores LU decomposition for solving linear systems, focusing on determinants and cofactors.

Finite Elements: Elasticity and Variational Formulation

Explores finite element methods for elasticity problems and variational formulations, emphasizing admissible deformations and numerical implementations.

Eigenvalues and Eigenvectors Decomposition

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

Factorisation LU

Explains Gaussian elimination and LU factorization for solving linear systems of equations.

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