Linear Algebra and Geometry 2

Linear Algebra and Geometry 2Much more about matrices; abstract vector spaces and their basesChapter 1: Abstract vector spaces and related stuffS1. Introduction to the courseS2. Real vector spaces and their subspacesYou will learn: the definition of vector spaces and the way of reasoning around the axioms; determine whether a subset of a vector space is a subspace or not.

S3. Linear combinations and linear independenceYou will learn: the concept of linear combination and span, linearly dependent and independent sets; apply Gaussian elimination for determining whether a set is linearly independent; geometrical interpretation of linear dependence and linear independence. S4.

Coordinates, basis, and dimensionYou will learn: about the concept of basis for a vector space, the coordinates w. r. t.

/ a given basis, and the dimension of a vector space; you will learn how to apply the determinant test for determining whether a set of n vectors is a basis of R^n. S5. Change of basisYou will learn: how to recalculate coordinates between bases by solving systems of linear equations, by using transition matrices, and by using Gaussian elimination; the geometry behind different coordinate systems.