Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

consider an eigenvalue $λ_{0}$ of an $n \times n$ matrix A. we are told that the algebraic multiplicity of exceeds 1. Show that $f' (λ_{0}) = 0$ (i.e.., the derivative of the characteristic polynomial of A vanishes are $λ_{0}$ ).

Consider an eigenvalue.

If an eigenvalue $λ_{0}$ of is of algebraic multiplicity greater than ,

it's at least 2.

$f' (λ) = 2 f (λ) (λ - λ_{0}) + f' (λ) (λ - λ_{0}) 2 f' (λ_{0}) = 0$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: definition of eigenvalues

The eigenvalue is a number that indicates how much variance exists in the data in that direction; in the example above, the eigenvalue is a number that indicates how spread out the data is on the line.

If an Eigenvalue $λ_{0}$ of is of algebraic multiplicity greater than 1,

it's at least 2.

So, the characteristic polynomial is,

Step 2: definition function

A function is a relationship between a set of inputs that each have one output.

A function is now, declare the values.

where is a function:

now,

. It is $f' (λ) = 2 f (λ) (λ - λ_{0}) + f' (λ) (λ - λ_{0}) 2 f' (λ_{0}) = 0$

Hence,

$f' (λ) = 2 f (λ) (λ - λ_{0}) + f' (λ) (λ - λ_{0}) 2 f' (λ_{0}) = 0$

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Linear Algebra With Applications

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Short Answer

consider an eigenvalue $λ_{0}$ of an $n \times n$ matrix A. we are told that the algebraic multiplicity of exceeds 1. Show that $f' (λ_{0}) = 0$ (i.e.., the derivative of the characteristic polynomial of A vanishes are $λ_{0}$ ).

Step by Step Solution

Step 1: definition of eigenvalues

Step 2: definition function

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Linear Algebra With Applications

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Short Answer

consider an eigenvalue λ0of an n×n matrix A. we are told that the algebraic multiplicity of exceeds 1. Show that f'(λ0)=0(i.e.., the derivative of the characteristic polynomial of A vanishes are λ0).

Step by Step Solution

Step 1: definition of eigenvalues

Step 2: definition function

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consider an eigenvalue $λ_{0}$ of an $n \times n$ matrix A. we are told that the algebraic multiplicity of exceeds 1. Show that $f' (λ_{0}) = 0$ (i.e.., the derivative of the characteristic polynomial of A vanishes are $λ_{0}$ ).