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.

Applications: 1

  1. Definition: Linear Combination
  2. Definition: Linearly Dependent and Linearly Independent Vectors, Zero Vector
  3. Definition: Dimension of a Vector Space
  4. Proposition: Quotient Space
  5. Definition: Generating Systems
  6. Definition: Basis, Coordinate System
  7. Definition: Exterior Algebra, Alternating Product, Universal Alternating Map
  8. Definition: Linear Span
  9. Section: Cross Product
  10. Section: Subspaces
  11. Section: Dual Space
  12. Definition: Linear Map
  13. Definition: Bilinear Form

Chapters: 1

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