# Vector Space (Review) by Rashad Wattu

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

### Download or View online

### Notes of other subjects

- Advance Analysis by Ms. Iqra Liaqat
- Advanced Analysis: Handwritten Notes
- Affine and Euclidean Geometry by Shahzad Idress
- Complex Analysis (Easy Notes of Complex Analysis)
- Complex Analysis (Notes) by Ms. Iqra Liaqat
- Complex Analysis (Quick Review)
- Complex Analysis by M Usman Hamid
- Computing Tools for Mathematics by Asif Arshad
- Differential Geometry (Notes) by Ms. Kaushef Salamat
- Differential Geometry by M Usman Hamid
- Differential Geometry by Syed Hassan Waqas
- Differential Geometry: Handwritten Notes
- Fluid Dynamics I by Muhammad Usman Hamid
- Fluid Mechanics I by Dr Rao Muzamal Hussain
- Fluid Mechanics II by Dr Rao Muzamal Hussain
- Functional Analysis by M Usman Hamid and Zeeshan Ahmad
- Functional Analysis by Mr. Tahir Hussain Jaffery
- Functional Analysis by Prof Mumtaz Ahmad
- Fundamental of Complex Analysis (Solutions of Some Exercises)
- Fuzzy Sets Theory by Umar Saeed Bunarai
- General Topology by Raheel Ahmad
- Handwritten Notes of Real Analysis by Asim Marwat
- History of Mathematics by Muhammad Usman Hamid
- Mathematical Method by Khalid Latif Mir (Solutions)
- Mathematical Method by Muhammad Usman Hamid
- Mathematical Method by Sir Muhammad Awais Aun
- Mathematical Statistics by Ms. Iqra Liaqat
- Mathematical Statistics I by Muzammil Tanveer
- Mathematical Statistics II by Sir Haidar Ali
- Measure Theory by M Usman Hamid & Saima Akram
- Measure Theory Notes by Anwar Khan
- Mechanics (Easy Notes of Mechanics)
- Mechanics by Sir Nouman Siddique
- Mechanics I (Statics) by Dr Babar Ahmad
- Method of Mathematical Physics by Mr. Muhammad Usman Hamid
- Metric Spaces (Notes)
- Multiple Choice Questions (BSc/BS/PPSC) by Akhtar Abbas
- Notes of Mathematics
- Number Theory by Dr Muhammad Umer Shuaib
- Number Theory by Ms. Iqra Liaqat
- Number Theory: Handwritten Notes
- Number Theory: Notes by Anwar Khan
- Numerical Analysis by M Usman Hamid
- Numerical Analysis II
- Operation Research by Sir Haidar Ali
- Operation Research: Handwritten Notes
- Partial Differential Equations
- Partial Differential Equations by M Usman Hamid
- Real Analysis (Notes by Prof. Syed Gul Shah)
- Ring (Notes) by Prof. M. Dabeer Mughal
- Rings & Modules by Ms. Iqra Liaqat
- Rings (Handwritten notes)
- Special Functions by Dr. Muhey-U-Din
- Theoretical Mechanics by Khalid Latif Mir (Solutions)
- Theory of Optimization by Ma'am Iqra Razzaq
- Topology and Functional Analysis Solved Paper by Noman Khalid
- Topology Notes by Azhar Hussain
- Topology: Handwritten Notes
- Vector Space (Review) by Rashad Wattu