Vol. 35, No. 1, 1970

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Rank preservers of skew-symmetric matrices

Marion-Josephine Lim

Vol. 35 (1970), No. 1, 169–174

It is possible to study the structure of rank preservers on n-square skew-symmetric matrices over an algebraically closed field F by considering instead the linear transformations on the second Grassmann Product Space 2𝒰 (𝒰 an n-dimensional vector space) over F into itself, which preserve the irreducible lengths of the products. In this paper, it is shown that preservers of irreducible length 2 are also preservers of all irreducible lengths of the products. Correspondingly, rank 4 preservers are rank 2k preservers for all positive integer values of k. The structure of the preservers in each case is deduced from the fact that these preservers are in particular irreducible length 1 and rank 2 preservers respectively, whose structures are known.

Mathematical Subject Classification
Primary: 15.30
Received: 16 May 1969
Published: 1 October 1970
Marion-Josephine Lim