Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree

• The set POLd,rm×n of m×n complex matrix polynomials of grade d and (normal) rank at most r in a complex (d+1)mn dimensional space is studied. For r=1,...,min{m,n}−1, we show that POLd,rm×n is the union of the closures of the rd+1 sets of matrix polynomials with rank r, degree exactly d, and explicitly described complete eigenstructures. In addition, for the full-rank rectangular polynomials, i.e. r=min{m,n} and m≠n, we show that POLd,rm×n coincides with the closure of a single set of the polynomials with rank r, degree exactly d, and the described complete eigenstructure. These complete eigenstructures correspond to generic m×n matrix polynomials of grade d and rank at most r.

Ämnesord

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Sciences (hsv//eng)

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

NATURVETENSKAP  -- Data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Complete eigenstructure

Genericity

Matrix polynomials

Normal rank

Orbits

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