Bandwidth has distinct meanings in matrix theory, graph theory, and signal processing.
The bandwidth of a matrix 
is the maximum value of 
such that 
is nonzero.
The graph bandwidth of a graph is the minimum bandwidth of its adjacency matrix over all orderings of the graph vertices.
For a signal whose Fourier transform vanishes outside a frequency interval ![[f_(min),f_(max)]](/images/equations/Bandwidth/Inline4.svg)
, the bandwidth is 
. More generally, an effective bandwidth is the
width of a stated frequency range in which the signal or system response satisfies
a specified criterion. The criterion matters when the spectrum does not vanish sharply.
The Shannon-Hartley theorem uses the bandwidth
of an ideal band-limited communication channel.
