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On the variation of co-ordinates in subspaces

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Summary

Let1≦k≦n−1, 2≦n. This paper examines the vectors δp(Lk), where Lk is a k-dimensional subspace of an n-dimensional space, and the co-ordinates of δp(Lk) are given below by (1.1).

For fixed k, the set of such vectors as Lk varies is determined for p=2. For general p, information is given on upper and lower bounds for the sum of the co-ordinates of δp(Lk).

References

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    Ky Fan andA. J. Hoffman, «Lower Bounds for the Rank and Location of the Eigenvalues of a Matrix », contribution to the Solution of Systems of Linear Equations and the Determination of Eigenvalues, edited by Olga Taussky, Nat. Bus. of Standards Appl. Math. Series 39 (1954), 117–130.

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    Alfred Horn, «Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix », American Journal Math., LXXVI (1954), 620–630.

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    A. M. Ostrowski, «Sur les conditions générales pour la régularité des matrices », Rend. di matem. e delle sue Appl. 10 (1951), 156–168.

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Additional information

Dedicated to the sixtieth birthday of Prof. Edgar R. Lorch

This research was supported in part by the Office of Naval Research under contract number Nonr 3775(09), NR 047040.

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Hoffman, A.J. On the variation of co-ordinates in subspaces. Annali di Matematica 86, 53–59 (1970). https://doi.org/10.1007/BF02415709

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Keywords

  • Lower Bound