Post on 26-Aug-2020
transcript
Vector Spaces: Handwritten notes
by
Atiq ur Rehman
http://www.MathCity.org/atiq
Partial Contents1. Rings; definition and examples 1
2. Field, definition and examples 1
3. Vector spaces, definition and examples 2
4. Subspaces, definition and related theorems 3
5. Linear sum, definition and related theorems 4
6. Homomorphism, kernel, linear combination 6
7. Linear span, related theorem 7
8. Finite dimensional vector space, linear dependent and independent, related theorem 8
9. Basis of a vector space and related theorems 10
10. Quotient space and related theorems 15
11. Internal direct sum, external direct sum, vector space homomorphism and relatedtheorems 19
12. Hom(V,W) and related theorems 26
13. Dual spaces and related theorems 32
14. Null space, nullity and related theorems 34
15. Eigen value, eigen vector, examples and related theorems 34
16. Characteristic polynomial/equation/matrix, examples and related theorem 46
17. Calay Hamilton theorem 48
18. Minimum polynomial (or minimal polynomial) and related theorems 50
19. Similar matrices and related theorems 55
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MathCity.org Merging man and maths
Vector Spaces (Handwritten notes) Written by: AWritten by: AWritten by: AWritten by: Atiq ur Rehman, Class: BS or MSc (Maths)tiq ur Rehman, Class: BS or MSc (Maths)tiq ur Rehman, Class: BS or MSc (Maths)tiq ur Rehman, Class: BS or MSc (Maths)
Available online at http://www.MathCity.org , Version: 1.0.0
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********************************************** Available online at http://www.MathCity.org
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Vector Spaces: Handwritten notes
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Vector Spaces: Handwritten notes
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Vector Spaces: Handwritten notes
• Home � http://www.mathcity.org
o FSc � http://www.mathcity.org/fsc
o BSc � http://www.mathcity.org/bsc
o MSc � http://www.mathcity.org/msc
o MPhil/PhD � http://www.mathcity.org/mphil-phd
o Old papers � http://www.mathcity.org/papers
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Vector Spaces: Handwritten notes
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********************************************** Available online at http://www.MathCity.org
**********************************************
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Vector Spaces: Handwritten notes
**********************************************
Available online at http://www.MathCity.org
**********************************************
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Vector Spaces: Handwritten notes
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Vector Spaces: Handwritten notes
• Home � http://www.mathcity.org
o FSc � http://www.mathcity.org/fsc
o BSc � http://www.mathcity.org/bsc
o MSc � http://www.mathcity.org/msc
o MPhil/PhD � http://www.mathcity.org/mphil-phd
o Old papers � http://www.mathcity.org/papers
o E-Books � http://www.mathcity.org/e-books
**********************************************
Available online at http://www.MathCity.org
**********************************************
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