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Concept

Collineation

Related lectures (20)

Covers isometries, transformations preserving distances and properties related to collinearity.

Introduces the axioms of connection in Euclidean geometry, emphasizing unique lines and non-collinear points.

Explains orthogonal projection and vector decomposition with examples in particle trajectory analysis.

Focuses on proving the Cellular Approximation Theorem, introducing polyhedra and piecewise linear maps.

Covers the analytical study of the plan, focusing on points and lines.

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Introduces vector definitions, displacement, addition, and applications in geometry.

Explores linear dependence of vectors, demonstrating examples and conditions for collinearity.

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Explores intersections of lines and medians in a square geometry context.

Explores base changes, bijective linear applications, matrix transformations, and dimensions of kernel and image spaces.

Explores guiding vectors in analytical geometry, emphasizing the importance of non-collinear and non-coplanar vectors in defining coordinate systems.

Explores the joint equidistribution of CM points and their properties in ergodic theory and homogeneous dynamics.

Covers the fundamentals of analytical geometry, focusing on vectors and their operations.

Covers landmarks, guiding vectors, and the abscissa concept in vector spaces.

Explains surface normals for parametric and implicit surfaces, focusing on vector analysis and examples with spheres.

Explores local-global duality in lattices and joint equidistribution of CM points.

Explores vector space properties, operations, linear combinations, and subspaces construction.

Explores chirality in space orientation, right hand rule, vectors properties, kinematics, and accelerations in physics.

Explores linear dependence and independence of vectors in geometric spaces.