Isometries in Euclidean Spaces

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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.