# Vector Spaces (Handwritten notes)

These are lecture notes of Prof. Dr. Muhammad Khalid of University of Sargodha, Sargodha written by Atiq ur Rehman. Please be careful while reading these notes as there might be some error while noting.

Name | Vector Spaces (Handwritten notes)- Lecture Notes |
---|---|

Author(s) | Atiq ur Rehman |

Pages | 58 pages |

Format | PDF (see Software section for PDF Reader |

Size | PDF: 2.75MB |

### CONTENTS OR SUMMARY:

- Rings; definition and examples
- Field, definition and examples
- Vector spaces, definition and examples
- Subspaces, definition and related theorems
- Linear sum, definition and related theorems
- Homomorphism, kernel, linear combination
- Linear span, related theorem
- Finite dimensional vector space, linear dependent and independent, related theorem
- Basis of a vector space and related theorems
- Quotient space and related theorems
- Internal direct sum, external direct sum, vector space homomorphism and related theorems
- Hom(V,W) and related theorems
- Dual spaces and related theorems
- Null space, nullity and related theorems
- Eigen value, eigen vector, examples and related theorems
- Characteristic polynomial/equation/matrix, examples and related theorem
- Calay Hamilton theorem
- Minimum polynomial (or minimal polynomial) and related theorems
- Similar matrices and related theorems

### Download or View online

### Notes of other subjects

- Advance Analysis by Ms. Iqra Liaqat
- Advanced Analysis: Handwritten Notes
- Algebra II by Syed Sheraz Asghar
- Complex Analysis (Easy Notes of Complex Analysis)
- Complex Analysis (Quick Review)
- Differential Geometry by M Usman Hamid
- Differential Geometry by Syed Hassan Waqas
- Differential Geometry: Handwritten Notes
- Fluid Mechanics I by Dr Rao Muzamal Hussain
- Fluid Mechanics II by Dr Rao Muzamal Hussain
- Functional Analysis by Mr. Tahir Hussain Jaffery
- Functional Analysis by Prof Mumtaz Ahmad
- Fundamental of Complex Analysis (Solutions of Some Exercises)
- General Topology by Raheel Ahmad
- Group Theory by Mr. Muhammad Iftikhar
- Group Theory: Important Definitions and Results
- Groups (Handwritten notes)
- Linear Algebra: Important Definitions and Results
- Mathematical Method by Sir Muhammad Awais Aun
- Mathematical Statistics I by Muzammil Tanveer
- Mathematical Statistics II by Sir Haidar Ali
- Measure Theory Notes by Anwar Khan
- Mechanics (Easy Notes of Mechanics)
- Mechanics by Sir Nouman Siddique
- Metric Spaces (Notes)
- Number Theory by Dr Muhammad Umer Shuaib
- 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
- Theory of Optimization by Ma'am Iqra Razzaq
- Theory of Relativity & Analytic Dynamics: Handwritten Notes
- Topology Notes by Azhar Hussain
- Topology: Handwritten Notes
- Vector Spaces (Handwritten notes)

- msc/notes/vector_spaces_handwritten_notes
- Last modified: 3 months ago
- by Dr. Atiq ur Rehman