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.

• 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

• Advance Analysis by Ms. Iqra Liaqat
• Advanced Analysis: Handwritten Notes
• Affine and Euclidean Geometry by Shahzad Idress
• Algebra II by Syed Sheraz Asghar
• Complex Analysis (Easy Notes of Complex Analysis)
• Complex Analysis (Notes) by Ms. Iqra Liaqat
• Complex Analysis (Quick Review)
• Complex Analysis by M Usman Hamid
• 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 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
• Group Theory by Mr. Muhammad Iftikhar
• Group Theory: Important Definitions and Results
• Groups (Handwritten notes)
• Handwritten Notes of Real Analysis by Asim Marwat
• Linear Algebra: Important Definitions and Results
• 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
• 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
• Theory of Relativity & Analytic Dynamics: Handwritten Notes
• Topology and Functional Analysis Solved Paper by Noman Khalid
• Topology Notes by Azhar Hussain
• Topology: Handwritten Notes
• Vector & Tensor Analysis by Dr Nawazish Ali (Solutions)
• Vector Space (Review) by Rashad Wattu
• Vector Spaces (Handwritten notes)