Orthogonal Planes and Rotations

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Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Explores linear dependence theorems and proofs, emphasizing the importance of understanding linear dependence in linear algebra.

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Explores linear applications, matrix-vector products, and the linearity of transformations.

Explores rotation in two dimensions, covering vector products, angular momentum, and kinetic energy of solids.

Covers the concept of 2D rotations and their analytical expressions.

Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.

Explores linear independence in vector spaces and the concept of bases.

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

Explains the concept of least squares solutions and their application in finding the closest solution to a system of equations.