Lectures related to Linear Algebra: Applications and Definitions

Introduces cardinality and mapping in linear algebra, illustrating concepts with examples and visual aids.

Covers Cartesian equations in analytical geometry, focusing on encoding line directions and unique equations.

Explores rotation in analytical geometry, including center coordinates and fixed points.

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Explores oriented angles in analytical geometry, discussing unit vectors, trigonometric functions, matrix representations, and rotations.

Explains equivalence in linear algebra and set calculations with illustrative examples.

Explores the properties of bisectors and areas in Analytical Geometry.

Explores reflections and translations in geometric transformations, demonstrating their stability and practical applications.

Explores orthogonal projections, symmetry of matrices, and their applications.

Covers Analytical Geometry, focusing on intersections and medians, providing step-by-step solutions for various cases.

Explores normal equations of lines in the plane through point translation for precision.

Covers the concept of enumeration and counting subsets of a finite set with examples and factorial notation.

Covers coordinates, midpoints, and abscissa in analytical geometry, providing practical problem-solving examples.

Explores the symmetry of vectors with respect to a line in Analytical Geometry.

Explores reflection and rotation composition in analytical geometry, including finding centers and solving fixed point systems.

Explores Cartesian equations for lines in a plane and their parametric descriptions.

Explores the Cartesian product in linear algebra and the method of induction for proving propositions.

Explores the locus of points in a square and angles between them.

Explores identical applications in linear algebra, discussing their representation and implications through examples and equation solving.

Explores parametric equations and their dependence on the choice of observation benchmarks.