Nonlinear eigenproblem

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a nonlinear eigenproblem, sometimes nonlinear eigenvalue problem, is a generalization of the (ordinary) <a href="/facts/Eigenvalue%2c_eigenvector_and_eigenspace/8TjEoT8u">eigenvalue problem</a> to equations that depend <a href="/facts/Nonlinearly/4aYItALC">nonlinearly</a> on the eigenvalue. Specifically, it refers to equations of the form

M
        (
        λ
        )
        x
        =
        0
        ,
      
    
    {\displaystyle M(\lambda )x=0,}

where 
 
 
 
 x
 ≠
 0
 
 
 {\displaystyle x\neq 0}
 
 is a <a href="/facts/Vector_(mathematics)/U8mM7A5F">vector</a>, and 
 
 
 
 M
 
 
 {\displaystyle M}
 
 is a <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a>-valued <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> of the number 
 
 
 
 λ
 
 
 {\displaystyle \lambda }
 
. The number 
 
 
 
 λ
 
 
 {\displaystyle \lambda }
 
 is known as the (nonlinear) eigenvalue, the vector 
 
 
 
 x
 
 
 {\displaystyle x}
 
 as the (nonlinear) eigenvector, and 
 
 
 
 (
 λ
 ,
 x
 )
 
 
 {\displaystyle (\lambda ,x)}
 
 as the eigenpair. The matrix 
 
 
 
 M
 (
 λ
 )
 
 
 {\displaystyle M(\lambda )}
 
 is singular at an eigenvalue 
 
 
 
 λ
 
 
 {\displaystyle \lambda }
 
.

Nonlinear eigenproblem open-in-new

Nonlinear eigenproblem