Lectures related to Isometries in R^n

Discusses isometries and orthonormal bases in mathematics.

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

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Explores the equivalence conditions for orthogonal matrices and includes examples of rotations.

Delves into modern geometry, covering transformations, isometries, and symmetries.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores isometries, reflections, rotations, and translations in space, as well as the structure theorem and configurations of planes and lines.

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

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

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers the theorems related to orthogonal projection and orthonormal bases.

Covers visualizations in orthonormal bases in R2, focusing on rotations and reflections.

Explores the composition of plane reflections and isometries in space, showcasing how reflections can lead to rotations and different isometries.

Covers the preservation of isometry by rotations and symmetries.

Explores the properties and applications of Euclidean isometries in R^2.

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

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Explores rotations as isometries composed of reflections with common axes and the flexibility in choosing rotation axes.