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Chapter 5

Chapter 5. Section 1. Theorem 5.1.1: If x and y are two nonzero vectors in either R 2 or R 3 and θ is the angle between them, then x T y =|| x |||| y ||cosθ. y -x. x. y. θ. Example. The projection of x onto y. x. y. θ. The projection of x onto y. x. y. θ.

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Chapter 5

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  1. Chapter 5 Section 1

  2. Theorem 5.1.1: If x and y are two nonzero vectors in either R2 or R3 and θ is the angle between them, then xTy=||x||||y||cosθ y-x x y θ

  3. Example

  4. The projection of x onto y x y θ

  5. The projection of x onto y x y θ

  6. The projection of x onto y x y θ u

  7. The projection of x onto y x y θ αu u

  8. The projection of x onto y x x-αu y θ αu u

  9. The projection of x onto y x x-αu y θ αu

  10. The projection of x onto y x x-αu y θ αu

  11. The projection of x onto y x x-αu y θ αu

  12. The projection of x onto y x x-αu y θ αu

  13. Example

  14. Example

  15. Example

  16. Example y=(1,2)T x=(5,2)T

  17. Equations of Planes

  18. Scalar Product: Distance: Angle: Orthogonal when: Extensions to Rn:

  19. Scalar Product: Distance: Angle: Orthogonal when: Extensions to Rn:

  20. Scalar Product: Distance: Angle: Orthogonal when: Extensions to Rn:

  21. Scalar Product: Distance: Angle: Orthogonal when: Extensions to Rn:

  22. Vectors inRn:

  23. Vectors inRn:

  24. Vectors inRn:

  25. Vectors inRn:

  26. Vectors inRn:

  27. Vectors inRn: If x and y are orthogonal….. y x x+y

  28. Search Engines Books: B1: Applied Linear Algebra B2: Elementary Linear Algebra B3: Elementary Linear Algebra with Applications B4: Linear Algebra and its applications B5: Linear Algebra with Applications B6: Matrix Algebra with Applications B7: Matrix Theory Keywords: algebra, application, elementary, linear, matrix, theory

  29. Search Engines Books: B1: Applied Linear Algebra B2: Elementary Linear Algebra B3: Elementary Linear Algebra with Applications B4: Linear Algebra and its applications B5: Linear Algebra with Applications B6: Matrix Algebra with Applications B7: Matrix Theory

  30. Search Engines

  31. Search Engines Words to Search For: Applied Linear Algebra

  32. Search Engines Words to Search For: Applied Linear Algebra

  33. Search Engines

  34. Search Engines B1: Applied Linear Algebra B2: Elementary Linear Algebra B3: Elementary Linear Algebra with Applications B4: Linear Algebra and its applications B5: Linear Algebra with Applications B6: Matrix Algebra with Applications B7: Matrix Theory

  35. Relative Frequency Searches

  36. Relative Frequency Searches

  37. Relative Frequency Searches

  38. Relative Frequency Searches

  39. Relative Frequency Searches Words to Search For: orthogonality spaces vector

  40. Relative Frequency Searches Words to Search For: orthogonality spaces vector Note: Since y5=0.635 is the entry ofythat is closest to 1, the direction of the search vectoruis closest to the direction of q5 and hence document 5 is the one that best matches our search criteria

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