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Chapter: Vectors Revised  Vector Spaces
So far, we have dealt with vectors in the context of solving linear equations. Before we continue our applications of vectors, it makes sense to pause dealing with applications and take a look at vectors from a higher perspective. It is necessary to learn more about one of the most important algebraic structures in mathematics strongly linked to vectors, called vector spaces and which we will now define formally.
Table of Contents
Applications: 1
 Definition: Linear Combination
 Definition: Linearly Dependent and Linearly Independent Vectors, Zero Vector
 Definition: Dimension of a Vector Space
 Proposition: Quotient Space
 Definition: Generating Systems
 Definition: Basis, Coordinate System
 Definition: Exterior Algebra, Alternating Product, Universal Alternating Map
 Definition: Linear Span
 Section: Cross Product
 Section: Subspaces
 Section: Dual Space
 Definition: Linear Map
 Definition: Bilinear Form
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Chapters: 1
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