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Numerical Methods in Engineering with Python 3, Third Edition by Jaan Kiusalaas

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9

Symmetric Matrix Eigenvalue Problems

 Find λ for which nontrivial solutions of Ax = λx exist. 

9.1 Introduction

The standard form of the matrix eigenvalue problem is

(9.1)

where A is a given n × n matrix. The problem is to find the scalar λ and the vector x. Rewriting Eq. (9.1) in the form

(9.2)

it becomes apparent that we are dealing with a system of n homogeneous equations. An obvious solution is the trivial one x = 0. A nontrivial solution can exist only if the determinant of the coefficient matrix vanishes; that is, if ...

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