vector spaces orhtogonalization
DESCRIPTION
.TRANSCRIPT
![Page 1: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/1.jpg)
10/10/2012
1
Mappings, Inner Product Spaces
& Orthogonalization
Vineet Sahula
Vector Spaces & Sub-Spaces
V. Sahula 2Vector Spaces
![Page 2: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/2.jpg)
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Vector Spaces & Sub-Spaces…
V. Sahula 3Vector Spaces
Vector Spaces & Sub-Spaces…
V. Sahula 4Vector Spaces
![Page 3: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/3.jpg)
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Basis & Dimension
V. Sahula 5Vector Spaces
Basis & Dimension…
V. Sahula 6Vector Spaces
![Page 4: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/4.jpg)
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Basis & Dimension…
V. Sahula 7Vector Spaces
Basis & Dimension…
V. Sahula 8Vector Spaces
![Page 5: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/5.jpg)
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Basis & Dimension…
V. Sahula 9Vector Spaces
Basis & Dimension…
V. Sahula 10Vector Spaces
![Page 6: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/6.jpg)
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Basis & Dimension…
V. Sahula 11Vector Spaces
Basis & Dimension…
V. Sahula 12Vector Spaces
![Page 7: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/7.jpg)
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Basis & Dimension…
V. Sahula 13Vector Spaces
Basis & Dimension…
V. Sahula 14Vector Spaces
![Page 8: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/8.jpg)
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Basis & Dimension…
V. Sahula 15Vector Spaces
Linear Mappings
V. Sahula 16Vector Spaces
![Page 9: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/9.jpg)
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Linear Mappings…
V. Sahula 17Vector Spaces
Linear Mappings…
V. Sahula 18Vector Spaces
![Page 10: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/10.jpg)
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Linear Mappings…
V. Sahula 19Vector Spaces
Linear Mappings…
V. Sahula 20Vector Spaces
![Page 11: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/11.jpg)
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Linear Mappings…
V. Sahula 21Vector Spaces
Linear Mappings…
V. Sahula 22Vector Spaces
![Page 12: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/12.jpg)
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Linear Mappings…
V. Sahula 23Vector Spaces
Linear Mappings…
V. Sahula 24Vector Spaces
![Page 13: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/13.jpg)
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Linear Mappings…
V. Sahula 25Vector Spaces
Linear Mappings…
V. Sahula 26Vector Spaces
![Page 14: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/14.jpg)
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Linear Mappings…
V. Sahula 27Vector Spaces
Matrices & Linear Operators
V. Sahula 28Vector Spaces
![Page 15: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/15.jpg)
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Matrices & Linear Operators…
V. Sahula 29Vector Spaces
Matrices & Linear Operators…
V. Sahula 30Vector Spaces
![Page 16: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/16.jpg)
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Matrices & Linear Operators…
V. Sahula 31Vector Spaces
Matrices & Linear Operators…
V. Sahula 32Vector Spaces
![Page 17: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/17.jpg)
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Matrices & Linear Operators…
V. Sahula 33Vector Spaces
Matrices & Linear Operators…
V. Sahula 34Vector Spaces
![Page 18: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/18.jpg)
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Matrices & Linear Operators…
V. Sahula 35Vector Spaces
Matrices & Linear Operators…
V. Sahula 36Vector Spaces
![Page 19: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/19.jpg)
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Matrices & Linear Operators…
V. Sahula 37Vector Spaces
Matrices & Linear Operators…
V. Sahula 38Vector Spaces
![Page 20: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/20.jpg)
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Matrices & Linear Operators…
V. Sahula 39Vector Spaces
Matrices & Linear Operators…
V. Sahula 40Vector Spaces
![Page 21: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/21.jpg)
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Matrices & Linear Operators…
V. Sahula 41Vector Spaces
Matrices & Linear Operators…
V. Sahula 42Vector Spaces
![Page 22: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/22.jpg)
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Inner Product Spaces & Operators
V. Sahula 43Vector Spaces
Inner Product Spaces & Operators…
V. Sahula 44Vector Spaces
![Page 23: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/23.jpg)
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Inner Product Spaces & Operators…
V. Sahula 45Vector Spaces
Inner Product Spaces & Operators…
V. Sahula 46Vector Spaces
![Page 24: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/24.jpg)
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Inner Product Spaces & Operators…
V. Sahula 47Vector Spaces
Inner Product Spaces & Operators…
V. Sahula 48Vector Spaces
![Page 25: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/25.jpg)
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Inner Product Spaces & Operators…
V. Sahula 49Vector Spaces
Inner Product Spaces & Operators…
V. Sahula 50Vector Spaces
![Page 26: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/26.jpg)
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Inner Product Spaces & Operators…
V. Sahula 51Vector Spaces
Inner Product Spaces & Operators…
V. Sahula 52Vector Spaces
![Page 27: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/27.jpg)
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Inner Product Spaces & Operators…
V. Sahula 53Vector Spaces
Inner Product Spaces & Operators…
V. Sahula 54Vector Spaces
![Page 28: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/28.jpg)
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Inner Product Spaces & Operators…
V. Sahula 55Vector Spaces
Inner Product Spaces & Operators…
V. Sahula 56Vector Spaces
![Page 29: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/29.jpg)
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Inner Product Spaces & Operators…
V. Sahula 57Vector Spaces
Inner Product Spaces & Operators…
V. Sahula 58Vector Spaces
![Page 30: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/30.jpg)
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Inner Product Spaces & Operators…
V. Sahula 59Vector Spaces
Inner Product Spaces & Operators…
V. Sahula 60Vector Spaces
![Page 31: Vector Spaces Orhtogonalization](https://reader034.vdocument.in/reader034/viewer/2022050802/563dbb44550346aa9aabb2e2/html5/thumbnails/31.jpg)
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Inner Product Spaces & Operators…
V. Sahula 61Vector Spaces