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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Alfred Horn, «Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix », American Journal Math., LXXVI (1954), 620–630.
A. M. Ostrowski, «Sur les conditions générales pour la régularité des matrices », Rend. di matem. e delle sue Appl. 10 (1951), 156–168.
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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