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# Chapter 5 - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Chapter 5' - salaam

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Presentation Transcript

### 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

y=(1,2)T

x=(5,2)T

Distance:

Angle:

Orthogonal when:

Extensions to Rn:

Distance:

Angle:

Orthogonal when:

Extensions to Rn:

Distance:

Angle:

Orthogonal when:

Extensions to Rn:

Distance:

Angle:

Orthogonal when:

Extensions to Rn:

Vectors inRn:

If x and y are orthogonal…..

y

x

x+y

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

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

Words to Search For:

Applied

Linear

Algebra

Words to Search For:

Applied

Linear

Algebra

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

Words to Search For:

orthogonality

spaces

vector

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