- Each
value of λ
corresponds to one or more
eigenfunctions. If
multiple linearly independent eigenfunctions have the same eigenvalue, the
eigenvalue is...
- an
infinite number of
eigenvalues each with a
unique eigenfunction, and that
these eigenfunctions form an
orthonormal basis of a
certain Hilbert space...
-
suitable Hilbert space are used to
study the
behavior of
eigenvalues and
eigenfunctions of
differential equations. For example, the Sturm–Liouville problem...
- energies). It is also
called energy eigenvector,
energy eigenstate,
energy eigenfunction, or
energy eigenket. It is very
similar to the
concept of
atomic orbital...
- In
applied mathematics, the
Hough functions are the
eigenfunctions of Laplace's
tidal equations which govern fluid motion on a
rotating sphere. As such...
-
function such as x ↦ e i x , {\displaystyle x\mapsto e^{ix},} is an
eigenfunction of the
differential operator − i d d x {\displaystyle -i{\frac {d}{dx}}}...
-
modes of
vibration of an
idealized circular drum head.
These modes are
eigenfunctions of a
linear operator on a
function space, a
common construction in functional...
- is an
orthonormal basis of the
Hilbert space L2 that
consists of the
eigenfunctions of the
autocovariance operator. FPCA
represents functional data in the...
- {\tfrac {d}{dx}}} , in
which case the
eigenvectors are
functions called eigenfunctions that are
scaled by that
differential operator, such as d d x e λ x =...
- to
multiplication in the
frequency domain. For all LTI systems, the
eigenfunctions, and the
basis functions of the transforms, are
complex exponentials...
