Tag: Linear Algebra

• Matrices and Linear Systems: Coordinate Representations of Linear Maps and the Structure of SolutionsIntroduces matrices as representations of linear maps, derives the product from composition, and shows the solutions of Ax = b form a particular solution plus the kernel.MathematicsLinear AlgebraUndergraduateLinear AlgebraMatricesRepresentation MatrixGaussian EliminationRank~48 min
• Vector Spaces and Linear Maps: From the Eight Axioms to the Rank-Nullity TheoremStarting from the eight axioms, we build subspaces, bases and dimension, prove the exchange lemma and the rank-nullity theorem, and test them on projections, differentiation and PCA.MathematicsLinear AlgebraUndergraduateLinear AlgebraVector SpacesBasis and DimensionLinear MapsRank-Nullity Theorem~44 min