Lectures related to Change of Variables Theorem

Linear Algebra: Implications and Equivalences

Explores implications and equivalences in linear algebra through examples and formal proofs.

Covers the l2-embeddability theorem, isometric embeddings, positive semidefinite matrices, and eigenvalues computation.

Covers orthogonal families and projections in vector spaces, including the Gram-Schmidt process.

Satellite Tracking: Geolocation and Map Projections

Explores satellite tracking for geolocation and map projections, discussing challenges in representing spherical surfaces on a plane and the effects of different projection systems.

Linear Algebra: Matrices and Operations

Covers the definition of 3x3 matrices, determinants, matrix operations, and invertibility.

Sarrus Rule: Determinant Calculation

Covers the Sarrus rule for calculating determinants of 3x3 matrices and the invertibility of matrices.

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.