Vector Spaces (Handwritten notes)

Vector space is a fundamental subject in mathematics. At the undergraduate and upper secondary levels, the concept of vector space is regarded as basic and fundamental. These are lecture notes of Prof. Dr. Muhammad Khalid of University of Sargodha, Sargodha written by Atiq ur Rehman.

• 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

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