Linear Systems: Choleski Factorisation

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

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

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

Covers matrix operations, focusing on the product and inverse of matrices.

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Covers matrix multiplication, properties, and inverses in linear algebra.

Explores matrix inversion, conditions for invertibility, uniqueness of the inverse, and elementary matrices for inversion.

Covers matrix operations and reduction to echelon form with practical examples.

Covers the analysis of local extrema and Hessians, focusing on the development of limit notations.

Introduces the Gauss elimination algorithm for solving linear systems with practical examples in Python.

Explores determinants, similarity invariance, Cramer's formula, and geometric interpretations in matrices.

Explores the diagonalizability of matrices, linear transformations, and matrix representations with practical examples.

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Covers phase portraits, eigenvalue decomposition, Jordan decomposition, and stable nodes in non-linear systems.

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