Norm, Dot Product, Orthogonality

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Covers basic notions of vector geometry, including scalar product, norm, and projection.

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

Explores curves, isometries, Bezier curves, and the Frenet coordinate system.

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.

Delves into mechanics, exploring the symmetrical top problem, degrees of freedom, and conservation of energy.

Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.

Explores diagonalization in symmetric matrices, emphasizing orthogonality and orthonormal bases.

Covers the local inversion theorem and uniqueness of solutions in a ball around a point.

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