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Analytic function of a matrix
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Related lectures (30)
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Nonlinearity: Methods and Examples
Explores nonlinearity in numerical flow simulation, covering linearization methods and practical examples.
Matrix Exponential: Properties and Justifications
Covers the properties of the matrix exponential and its justification through the norm definition.
Networked Control Systems: Challenges and Opportunities
Explores challenges and opportunities in networked control systems, covering LTI systems, delays, packet drops, and consensus.
Diagonalization of Matrices
Explores the method of diagonalization for matrices and the calculation of matrix powers.
Gram-Schmidt Process and QR Decomposition
Covers the Gram-Schmidt process, QR decomposition, orthogonal projection theorem, and matrix formulas.
Matrix Similarity and Diagonalization
Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.
Square Matrices: Invertible, Triangular, Diagonal
Explains square matrices, including invertible, triangular, and diagonal matrices, and their properties.
Integral Curves and Exponential Map
Explores integral curves on manifolds and the significance of the exponential map in Lie groups.
Singular Value Decomposition: Applications and Interpretation
Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.
Convex Functions: Theory and Applications
Explores convex functions, including checking convexity, transformations, examples, minimization, geometric intuition, Schur's Lemma, distance function, perspective function, and relative entropy.