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Spectral radius
The
spectral radius
of a
matrix
or a
bounded linear operator
is the supremum among the
moduli
of the elements in its
spectrum
, which is sometimes denoted by ρ(·).
Table of contents
1 Matrix
2 Bounded linear operator
3 External links
Matrix
Let λ
_{1}
,...,λ
_{n}
be the (real or complex) eigenvalues of a matrix
A
. Then
ρ(
A
) := ρ(
A
) = max(λ
_{i}
)
The
spectral radius
of a
planar graph
is the spectral radius of its
adjacency matrix
.
For any
matrix norm
·, we have
ρ(
A
)=lim
_{n→∞}
A
^{n}

^{1/n}
.
Bounded linear operator
For a bounded linear operator
A
and the
operator norm
·, again we have
ρ(
A
)=lim
_{n→∞}
A
^{n}

^{1/n}
.
External links
Spectral Radius of Planar Graphs