Lectures related to Isometries in Euclidean Spaces

Isometries & Orientation in Modern Geometry

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

Symmetry in Modern Geometry

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

Matrices and Orthogonal Transformations

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

Isometries: Definition and Examples

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

Isometries and Orthonormal Bases

Discusses isometries and orthonormal bases in mathematics.

Symmetry in the Plane

Explores the modern definition of symmetry and its practical applications.

Rotations and Symmetries

Covers the preservation of isometry by rotations and symmetries.

Symmetries of Navier-Stokes Equations

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

2D Transformations: Linear Maps & Matrices

Covers 2D transformations, linear maps, matrices, affine transformations, and orthogonal transformations.

Geometric Transformations in R2 and R3: Visualizations and Rotations

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

Isometries & Orientation: Modern Symmetry

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

Symmetry in Modern Geometry

Explores symmetry in modern geometry, focusing on isometries, reflections, rotations, and translations, emphasizing the importance of 180-degree rotations.

Symmetries of the Wave Equation

Explores the symmetries of the wave equation under Lorentz transformations and the Poincare group.

Linear Applications: Matrices and Transformations

Covers linear applications, matrices, transformations, and the principle of superposition.

Orthogonality and Subspace Relations

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Linear Applications Composition

Covers the composition of linear applications in R-vector spaces with fixed bases.

Orthogonality and Projection

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

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Discrete Symmetries: Asymptotic States and S-matrix

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

Linear Applications and Eigenvectors

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.