Miniversal deformations of pairs of skew-symmetric matrices under congruence

• Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair (A, B) we provide a normal form with a minimal number of independent parameters to which all pairs of skew-symmetric matrices ((A) over tilde (,) (B) over tilde), close to (A, B) can be reduced by congruence transformation which smoothly depends on the entries of the matrices in the pair ((A) over tilde (,) (B) over tilde). An upper bound on the distance from such a miniversal deformation to (A, B) is derived too. We also present an example of using miniversal deformations for analyzing changes in the canonical structure information (i.e. eigenvalues and minimal indices) of skew-symmetric matrix pairs under perturbations.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Skew-symmetric matrix pair

Skew-symmetric matrix pencil

Congruence canonical form

Congruence

Perturbation

Versal deformation

Publication and Content Type

ref (subject category)

art (subject category)