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Jordan Normal FormCovers the Jordan Normal Form and the identification of torsion blocks within matrices.
Cyclic Subspace DecompositionExplores minimal annihilating polynomials and cyclic invariant subspaces, showcasing their practical applications through matrix computations.
Jordan Normal FormCovers the Jordan Normal Form theorem and invariance of kernels under transformations.
Smith Normal FormCovers the concept of Smith Normal Form for integer matrices and its uniqueness conditions.
Exponential of Operators and MatricesCovers the exponential of operators and matrices, commutation properties, Jordan normal form, and linear algebra concepts related to linear operators and eigenvalue problems.
Magnetic MomentsCovers magnetic moments, Ampère's law, and Biot-Savart's law applications.
Linear Algebra: DiagonalizationExplores the diagonalization of matrices and the conditions for exact diagonalization, with examples demonstrating the process.