Vol. 75, No. 2, 1978

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Intersections of the space of skew-symmetric maps with its translates

Daniel Byron Shapiro

Vol. 75 (1978), No. 2, 553–560
Abstract

For a quadratic space V over a field K, let ℒ⊆ End(V ) be the space of all maps which are skew-symmetric wilh respect to the inner product. For g GL(V ), let 𝒟(g) = dim(ℒ∩g). In this paper we determine the largest few values possible for 𝒟(g), and we classify the maps g which achieve these values. The restriction of this result to maps g in the orthogonal group 𝒪(V ) generalizes the characterization of ± symmetries originally proved by Botta and Pierce.

Mathematical Subject Classification 2000
Primary: 15A63
Milestones
Received: 20 March 1977
Published: 1 April 1978
Authors
Daniel Byron Shapiro