On the variation of co-ordinates in subspaces

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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).


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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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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).

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