Vector Spaces (Handwritten notes)

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