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

Ernst Dieterich. "Existence and construction of two-dimensional invariant subspaces for pairs of rotations." Colloquium Mathematicae 114.2 (2009): 203-211. <http://eudml.org/doc/284228>.

@article{ErnstDieterich2009,
abstract = {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.},
author = {Ernst Dieterich},
journal = {Colloquium Mathematicae},
keywords = {pair of rotations; invariant subspace; commutator determinant; skew-symmetric matrix; division algebras; Euclidean space; orthogonal linear operator},
language = {eng},
number = {2},
pages = {203-211},
title = {Existence and construction of two-dimensional invariant subspaces for pairs of rotations},
url = {http://eudml.org/doc/284228},
volume = {114},
year = {2009},
}

TY - JOUR
AU - Ernst Dieterich
TI - Existence and construction of two-dimensional invariant subspaces for pairs of rotations
JO - Colloquium Mathematicae
PY - 2009
VL - 114
IS - 2
SP - 203
EP - 211
AB - 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.
LA - eng
KW - pair of rotations; invariant subspace; commutator determinant; skew-symmetric matrix; division algebras; Euclidean space; orthogonal linear operator
UR - http://eudml.org/doc/284228
ER -