Coxeter groups: reflections, rotations

Related lectures (31)

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

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

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

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

Covers the composition of geometric transformations in 2D, focusing on rotations and reflections to achieve specific results.

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

Explores geometric transformations in R2 and R3, including reflections, rotations, and practical applications like billiards.

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

Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.

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

Covers the topic of conformal transformations, including translations, dilations, rotations, and the conformal algebra.

Covers angular momentum in rotations, including preservation of angles and vector products.

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

Explores the normalization of the product of 4 plane reflections in space.

Covers the concept of orientation in the plane and transformations using matrices.

Explores changing bases for rotations, orthogonal planes, and vector transformations under rotation.

Explores isometries in space, transformations preserving lengths and angles, including reflections, rotations, and translations.

Explores Coxeter groups, reflections, fundamental regions, and classification by Coxeter graphs.

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

Explores eigenvalues of Coxeter elements, cyclic permutations, invariance, and decomposition of eigenspaces.

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