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[1] Suppose that $ \\|S \\| < 1 $. Take any nonzero vector $ x $, and let $ r := \\|x\\| $. We have $ \\| Sx \\| = r \\| S (x/r) \\| \\leq r \\| S \\| < r = \\| x\\| $. Hence every point is pulled towards the origin." ] } ], "metadata": { "filename": "linear_algebra.rst", "kernelspec": { "display_name": "Julia 1.2", "language": "julia", "name": "julia-1.2" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.2.0" }, "title": "Linear Algebra" }, "nbformat": 4, "nbformat_minor": 2 }