Lectures related to Orthogonal Planes and Rotations

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Explores finding particular solutions for homogeneous differential equations, emphasizing linear independence and variation of constants.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Covers the solutions of homogeneous linear differential equations and how to find linearly independent solutions.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Explores linear dependence and independence of vectors in geometric spaces.

Covers the general solution of inhomogeneous differential equations and explores linear dependence, uniqueness theorems, and second-order equations.

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.