1 research outputs found
Perturbation analysis of a matrix differential equation
Two complex matrix pairs and are contragrediently
equivalent if there are nonsingular and such that
. M.I. Garc\'{\i}a-Planas and V.V. Sergeichuk
(1999) constructed a miniversal deformation of a canonical pair for
contragredient equivalence; that is, a simple normal form to which all matrix
pairs close to can be reduced by
contragredient equivalence transformations that smoothly depend on the entries
of and . Each perturbation of defines the first order induced perturbation
of the matrix , which is the first order
summand in the product . We find all
canonical matrix pairs , for which the first order induced perturbations
are nonzero for all nonzero perturbations in
the normal form of Garc\'{\i}a-Planas and Sergeichuk. This problem arises in
the theory of matrix differential equations , whose product of two
matrices: ; using the substitution , one can reduce by
similarity transformations and by contragredient equivalence
transformations