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30 Aug 2019: STATIONERY REQUIREMENTS SPECIAL REQUIREMENTSCover sheet Triangle and squared paperTreasury TagScript paper. ... ii) If h is the set of diagonal elements in so5, and Li : h C is the usual linearmap sending a diagonal matrix to the iith entry, give the

30 Aug 2019: D be the diagonal matrix whose entries are 1/|CG(xi)|, as xiranges through representatives of the p′-classes. ... Show that Π̄DXT = I and deduce that X̄T Π is the diagonal matrix with entries|CG(xi)|, where the xi are representatives of the p.

30 Aug 2019: The questions carry equal weight. STATIONERY REQUIREMENTS SPECIAL REQUIREMENTS. Cover sheet None. ... a) Let P be a NYT, with x 6 P. Let Pi,j stand for the (i, j) entry of P.

12 Jul 2023: STATIONERY REQUIREMENTS SPECIAL REQUIREMENTSCover sheet NoneTreasury tagScript paperRough paper. You may not start to read the questionsprinted on the subsequent pages untilinstructed to do so by the Invigilator. ... In addition, L has O(n) non-zero

26 Nov 2019: at Cambridge, and funders’ research data sharing requirements and the support available in the University of Cambridge. ... Information on these requirements can be found on the University’s Research Operations webpage.

17 Jun 2019: STATIONERY REQUIREMENTS. Gold cover sheet. Green master cover sheet. You may not start to read the questions. ... Use the theorems you statedin (i) to prove that A has an eigenvector with positive entries.

17 Jun 2019: Consider a Q-matrix Q = (qij ) with entries. qij ={rj, i 6= j,R ri, i = j,. ... What property of thevector with entries πj relative to the matrix Q is involved here?

17 Jun 2019: STATIONERY REQUIREMENTS. Gold cover sheet. Green master cover sheet. You may not start to read the questions. ... Let SL2(Z) be the group of all 2 2 matriceswith integer entries and determinant 1.

17 Jun 2019: Deduce that any function f : V R suchthat f(A) is a polynomial in the entries of A is continuously differentiable. ... Byconsidering d(I H) as a polynomial in the entries of H, show that the derivative d′(I) isthe function H 7 tr H.

26 Nov 2019: Postgraduate Open Day On Wednesday 2nd November the Graduate Office are hosting the first ever Postgraduate Open Day in the Faculty of Mathematics. ... 30pm the Postgraduate Open Day will be taking place in half of the.