The geometry of the set of scaled projections

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The set of scaled projections of a vector onto the column space of a matrix has recently been of interest to several authors. The aim of the present investigation is to obtain a detailed description of the geometry of this set. In our main result we show by construction that the set of scaled projections is the union of finitely many polytopes. The proof makes use of a theorem on the alternative. © 1993.




Hanke, M., & Neumann, M. (1993). The geometry of the set of scaled projections. Linear Algebra and Its Applications, 190(C), 137–148.

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