Search

12 Mar 2019: Part IB GEOMETRY (Lent 2019): Example Sheet 3. (jb128@dpmms.cam.ac.uk). 1. Let V be the open subset {0 < u < π, 0 < v < 2π}, and σ : V S2 be given by. σ(u, v) = (sin u cos v, sin u sin v, cos u). Prove that σ defines a smooth parametrization of

14 Feb 2007: "!$#&%')(,.-0/214356,8793:<;='>:(?4@ ,.ACBED>79FG?4@IHKJ+@@LNM. OPQP RSUT">RQVWRXKYZ[U 0] Y_a[bcdRSe"fKRSWgh[ P RSi P RXY_]RQejRQk_RSml. n op deWUdKWqi bkb[UYZrjsturvj]wxW0 ... u P __z]w9rIRX0U ]_UR|wdzw" 08 n WdfWdRSwzRXKR P i.]_UWghRXK[RS[KWU]W n) z]Uk

15 Oct 2021: We clearly have that for any non-zero x Rn:. ||Ax|| ||A||op. ... x||. holds for any x and thus||An||op. ||A||. nop. Definition 29.

21 Nov 2016: 10. Let f : Rn Rn be a C1 map. Suppose that there is some constant µ < 1 such that‖Df|x I‖op µ for all x Rn.

13 Feb 2006: "$#&%')(,.-0/214356,8793:<;='>:(?4@ ,.ACBED>79FG?4@IHKJ+@@LNM. OPQP RSUT>RQVWRXKYZ[U 0] Y_a[bcdRSefKRSWgh[ P RSi P RXY_]RQejRQk_RSmln op deWUdKWqi bkb[UYZrjsturvj]wxW0 RSUTKr0sdyrvjRXz ... nK h j[RS}RQRSR>op deWU]KW0R P i_ P z>w VRXkb P RQgrh}RQeb

21 May 2005: OP , where O denotes the origin. (2) Let V be the open subset {0 < u < π, 0 < v < 2π}, and σ : V S2 be given by.

1 Mar 2018: OP , where O denotes the origin. 3. Show the stereographic projection map π : S {N} C, where N denotes the northpole, defines a chart.

21 Feb 2011: vector OP , where O denotes the origin.

17 Feb 2010: Part IB GEOMETRY, Examples sheet 3 (Lent 2010, Burt Totaro). (1) Show that the tangent space to S2 at a point P = (x, y, z) S2 is the plane. normal to the vectorOP , where O denotes the origin. (2) Let V be the open subset {0 < u < π, 0 < v < 2π}

2 Mar 2017: OP , where O denotes the origin. 3. Show the stereographic projection map π : S {N} C, where N denotes the northpole, defines a chart.