The Algebraic Eigenvalue Problem
by numerical-methods.com
The algebraic eigenvalue problem refers to finding a set of
characteristic values associated with a matrix or matrices.
Eigenvalues and eigenvectors are important in that when the
corresponding equations model a physical situation they tell
us useful information about it.
However the eigenvalue problem can take several different forms.
Tutorials on Matrix Eigenvalues
Traditional Eigenvalue Problem
The traditional eigenvalue problem involves finding the (eigen)values
l
and the (eigen)vectors x that are non-trivial solutions of
where A is an NxN matrix and x is an N-vector.
Generalised Eigenvalue Problem
The generalised eigenvalue problem involves finding the (eigen)values
l
and the (eigen)vectors x that are non-trivial solutions of
where A and B are an
N ×N matrix and x is an N-vector. Note that if
B = I, the identity matrix, then this is the traditional
eigenvalue problem.
Non-Linear Eigenvalue Problem
The non-linear eigenvalue problem involves finding the (eigen)values
l
and the (eigen)vectors x
that are non-trivial solutions of
where A is an N ×N matrix with each component of A being a
function of the parameter l.
Note that A(l) = C-lI then we have the
traditional eigenvalue problem and if A(l) = C- lD
then we have the generalised eigenvalue problem.
[boundary-element-method.com ] [electromagnetics.info] [ cad-cam-cae.com ] [ finite-element-method.info]
[AppliedMathematics.info ]
[Fortran ]
[science-books.net ]
[mathematics.me.uk] [computing.me.uk] [engineering.me.uk]
[physics.me.uk]
[statistics.me.uk]