Chapter 5
Download
1 / 40

Chapter 5 - PowerPoint PPT Presentation


  • 70 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Chapter 5' - salaam


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Chapter 5

Chapter 5

Section 1


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



The projection of x onto y

x

y

θ


The projection of x onto y

x

y

θ


The projection of x onto y

x

y

θ

u


The projection of x onto y

x

y

θ

αu

u


The projection of x onto y

x

x-αu

y

θ

αu

u


The projection of x onto y

x

x-αu

y

θ

αu


The projection of x onto y

x

x-αu

y

θ

αu


The projection of x onto y

x

x-αu

y

θ

αu


The projection of x onto y

x

x-αu

y

θ

αu





Example

y=(1,2)T

x=(5,2)T



Scalar Product:

Distance:

Angle:

Orthogonal when:

Extensions to Rn:


Scalar Product:

Distance:

Angle:

Orthogonal when:

Extensions to Rn:


Scalar Product:

Distance:

Angle:

Orthogonal when:

Extensions to Rn:


Scalar Product:

Distance:

Angle:

Orthogonal when:

Extensions to Rn:







Vectors inRn:

If x and y are orthogonal…..

y

x

x+y


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


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



Search Engines

Words to Search For:

Applied

Linear

Algebra


Search Engines

Words to Search For:

Applied

Linear

Algebra



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






Relative Frequency Searches

Words to Search For:

orthogonality

spaces

vector


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


ad