Abstract
The purpose of this note is to give a short proof of the theorem of Ralph in Linear Algebra Appl. 178 (1993), 249–260, on the geometry of projection maps. This theorem implies that the so-called normal maps derived from projections satisfy a general geometric criterion for bijectivity of piecewise affine maps given by Kuhn and Löwen in Linear Algebra Appl. 96 (Section 5.3), (1987), 109–129. As a consequence, one obtains Robinson's characterization of bijectivity of normal maps.
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References
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Ralph, D.: A new proof of Robinson's homomorphism theorem for piecewise linear normal maps, Linear Algebra Appl. 178 (1993), 249- 260.
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Löwen, R. Branching Numbers for Euclidean Projections onto Convex Polyhedra. Geometriae Dedicata 72, 99–103 (1998). https://doi.org/10.1023/A:1005051314227
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DOI: https://doi.org/10.1023/A:1005051314227