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# Vector Spaces (Handwritten notes)

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: 3.32MB |

### 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 LINKS

**Vector_Spaces_Handwritten_Notes.pdf ~ 3.32 MB**

**To view online [View Online]**

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- Ring (Notes) by Prof. M. Dabeer Mughal
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- msc/notes/vector_spaces_handwritten_notes
- Last modified: 7 weeks ago
- by Administrator