Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Consider a quadratic form
$q (\overset{⇀}{x}) = \overset{⇀}{x} . A \overset{⇀}{x}$
where A is a symmetric nxn matrix. Let $\overset{⇀}{v}$ be a unit eigenvector of A, with associated eigenvalue $λ$ . Find $q (\overset{⇀}{v})$ .

$q (\overset{⇀}{v}) = λ$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information:

$q (\overset{⇀}{x}) = \overset{⇀}{x} . A \overset{⇀}{x}$

Step 2: Determining q(v⇀):

Take a look at the quadratic form:

$q (\overset{⇀}{x}) = \overset{⇀}{x} . A \overset{⇀}{x}$

A is a nxn symmetric matrix. Let $\overset{⇀}{v}$ be the unit eigenvector of A, with lambda as the eigenvalue. Now, use the following formula to access $q (\overset{⇀}{v})$ :

role="math" localid="1659615170927" $q (\overset{⇀}{v}) = \overset{⇀}{v} . A \overset{⇀}{v} = \overset{⇀}{v} . λ \overset{⇀}{v} = λ (\overset{⇀}{v} . \overset{⇀}{v}) = λ (1)$

(According to the eigen value definition)

$\Rightarrow q (\overset{⇀}{v}) = λ$

Step 3: Determining the Result:

$q (\overset{⇀}{v}) = λ$

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

Consider a quadratic form
$q (\overset{⇀}{x}) = \overset{⇀}{x} . A \overset{⇀}{x}$
where A is a symmetric nxn matrix. Let $\overset{⇀}{v}$ be a unit eigenvector of A, with associated eigenvalue $λ$ . Find $q (\overset{⇀}{v})$ .

Step by Step Solution

Step 1: Given Information:

Step 2: Determining q(v⇀):

Step 3: Determining the Result:

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

Consider a quadratic form q(x⇀)=x⇀.Ax⇀where A is a symmetric nxn matrix. Let v⇀ be a unit eigenvector of A, with associated eigenvalue λ. Find q(v⇀).

Step by Step Solution

Step 1: Given Information:

Step 2: Determining q(v⇀):

Step 3: Determining the Result:

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

Consider a quadratic form
$q (\overset{⇀}{x}) = \overset{⇀}{x} . A \overset{⇀}{x}$
where A is a symmetric nxn matrix. Let $\overset{⇀}{v}$ be a unit eigenvector of A, with associated eigenvalue $λ$ . Find $q (\overset{⇀}{v})$ .