Signature of a Symmetric Matrix
The signature of a real symmetric matrix is the pattern of signs of the ordered determinants of the leading principal minors of .
Definition 9.6 (Signature)
The signature of is the parttern of signs of the ordered determinants of the leading principal minors of .
Leading principal minors
For a function , the signature is given by the signs of
the determinants of the leading principal minors of the Hessian matrix. Denoting these determinants , the last of them is the full determinant .
For example, at the stationary point of ,
giving the signature , while at ,
giving the signature .
Related
Stated in
- Definition 9.6 (Signature)§9.3.2 Nature of Stationary Points and the Hessian