Existence and construction of two-dimensional invariant subspaces for pairs of rotations

• Autorzy: Ernst Dieterich
• Języki publikacji: EN

Abstrakty

EN

By a rotation in a Euclidean space V of even dimension we mean an orthogonal linear operator on V which is an orthogonal direct sum of rotations in 2-dimensional linear subspaces of V by a common angle α ∈ [0,π]. We present a criterion for the existence of a 2-dimensional subspace of V which is invariant under a given pair of rotations, in terms of the vanishing of a determinant associated with that pair. This criterion is constructive, whenever it is satisfied. It is also used to prove that every pair of rotations in V has a 2-dimensional invariant subspace if and only if the dimension of V is congruent to 2 modulo 4.

Kategorie tematyczne

• 22E60: Lie algebras of Lie groups
• 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation
• 15A15: Determinants, permanents, other special matrix functions
• 17A80: Valued algebras
• 17A35: Division algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 114
• Numer: 2
• Strony: 203-211

Daty

wydano

2009

Twórcy

autor

Ernst Dieterich

• Uppsala universitet, Box 480, SE-751 06 Uppsala, Sweden

Identyfikatory

DOI

10.4064/cm114-2-4