# Vector Space (Review) by Rashad Wattu

Mathematical vector space is a crucial and fundamental idea. It depends on the concept of field. These notes were primarily written to help maths students understand vector space, which is a concept that they all need to be familiar with.

We are very thankful to Rashad Wattu for providing these notes and appreciates his effort to publish these notes on MathCity.org

Name | Vector Space (Review) |
---|---|

Author | Mr. Rashad Wattu |

Writer | Ms. Hadiqa Mumtaz |

Pages | 37 pages |

Format | PDF (see Software section for PDF Reader) |

Size | 4.96 MB |

### Contents or Summary:

- Definition: Vector Space
- Examples
- Subspace, examples, trivial subspace, non-trivial subspace
- Union of subspaces
- Intersection of subspaces
- Sum of subspaces
- Direct sum
- Linear combination and spanning sets
- Spanning sets
- Null spaces
- Column spaces
- Linear transformation
- Linearly independent sets
- Linearly dependent sets
- Basis and dimension
- Finite dimension vector space.
- Finite and infinite dimension vector space.
- Spanning set theorem
- Rank theorem
- Invertible matrix theorem
- Eigen values and eigen vectors
- Eigen space
- Orthogonal matrix