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Compounds of Skew-Symmetric Matrices

Published online by Cambridge University Press:  20 November 2018

Marvin Marcus  and
Adil Yaqub
Marvin Marcus
Affiliation:
University of California, Santa Barbara
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In a recent interesting paper (3) H. Schwerdtfeger answered a question of W. R. Utz (4) on the structure of the real solutions A of A* = B, where A is skew-symmetric. (Utz and Schwerdtfeger call A* the "adjugate" of A ; A* is the n-square matrix whose (i, j) entry is (—1)i+j times the determinant of the (n — 1)-square matrix obtained by deleting row i and column j of A. The word "adjugate," however, is more usually applied to the matrix (AT)*, where AT denotes the transposed matrix of A ; cf. (1, 2).)

The object of the present paper is to find all real n-square skew-symmetric solutions A to the equation

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 473 - 478
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Aitken, A. C., Determinants and matrices (Edinburgh, 1948).Google Scholar
2. Muir, T., A treatise on the theory of determinants (New York, 1960).Google Scholar
3. Schwerdtfeger, H., On the adjugate of a matrix, Portugal. Math., 20 (1961), 39–41.Google Scholar
4. Utz, W. R., Some theorems and questions on matrices, Portugal. Math., 18 (1959), 225–229.Google Scholar
5. Wedderburn, J. H., Lectures on matrices, Am. Math. Soc, Coll. Publ., 17 (1934).Google Scholar