Sylvester's Law Of Inertia
In
linear algebra
,
Sylvester's law of inertia
states that the inertia of a
matrix
A
is
invariant
under
congruence transformations
. It is named for
J. J. Sylvester
. The inertia of
A
is defined as the triple containing the numbers of positive, negative and zero
eigenvalues
of
A
: see also
signature (quadratic form)
. A congruence transformation of
A
is formed as the product
SAS^T
where
S
is any given
non-singular matrix
. In other words, the signature of
A
as
quadratic form
is
well-defined
and independent of
change of basis
.
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