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Extension of a theorem of C. G. F. James

Published online by Cambridge University Press:  24 October 2008

D. W. Babbage
D. W. Babbage
Affiliation:
Magdalene College
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Extract

The linear subspaces [k] of a space [n] have been represented by Grassmann by the points of a rational locus V(n−k)(k+1), of dimension (n−k)(k+1), in ; the representation is effected by taking as independent homogeneous coordinates of a [k] in [n] the determinants of order k+1 which belong to the matrix, of k+1 rows and n+1 columns, formed by the co-ordinates of any k+1 linearly independent points of the [k].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 4 , October 1932 , pp. 421 - 426
Copyright
Copyright © Cambridge Philosophical Society 1932

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References

* See Segre, , Encyk. der Math. Wiss., iii C 7, p. 791.Google Scholar

† Brown, L. M., Journal Lond. Math. Soc., 5 (1930), 168–176.CrossRefGoogle Scholar

‡ A [k] is said to be chordal to a given curve when it meets it in k + 1 points.

§ James, C. G. F., Proc. Camb. Phil. Soc., 21 (1923), 664.Google Scholar

* This theorem has been given by MissTelling, H. G., Proc. Camb. Phil. Soc., 28 (1932), 403–415.CrossRefGoogle Scholar