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4 Dec 2014: 1. The square matrices A and B over the field F are congruent if B = PTAP for some invertible matrixP over F. ... 7. Let S be an nn real symmetric matrix with Sk = I for some k 1.

24 Jan 2014: Xn be independent Poisson random variables, with Xi having meaniθ, for some θ > 0. ... b) For some n > 2, let X1,. ,Xn be iid with Xi Exponential(θ).

18 Sep 2014: components. Consider a map. : 1()! Z=pZ. for some prime p that maps all the boundary. ... If G F and H G then H is. measure-equivalent to some free group.

11 May 2014: AB| = |A| |B| 1. This looks fair enough, and in some sense it is, but we need to be clear aboutthe conventions we are using. ... All this is well and good, but it can cause some confusionwhen we start thinking about expressions like: |AB|.

16 Jul 2014: that the transition functions ψi ψ1j are in factaffine linear transformations v 7 Tv v0 for some T GL(Λ) andv0 V. ... This conjecture remains unproven other than some verystraightforward cases (abelian varieties, K3 surfaces).However, it has led to a

18 Jul 2014: Two. models Φ and Φ′ are R-equivalent if Φ′ = [A,B]Φ for some A,B GL5(R). ... If Φ′ = [A,B]Φ for some A,B GL5(K) then A,B K GL5(OK).In particular.

17 Mar 2014: There is some overlap between these examples andthe examples in my lecture notes. ... 6. This example arose from some psychiatry data provided by Professor I.Goodyerof Cambridge University.

10 Feb 2014: 3. An element r of a ring R is nilpotent if rn = 0 for some n. ... 6. Let A and B be elements of the power-set ring P(S), for some set S.

16 Apr 2014: Since B() is a local ring, it follows that. B() = (̂̃Ai,mi,k)() for some pair (i,k) which is uniquely determined by , and then = ri,k. ... GB ιχv,1 ιχv,n, for some smooth. characters χv,i : Fv Q.

24 Feb 2014: domain. Could there be some other Euclidean function φ making Z[3] into a Euclidean. ... Does it follow that the ring R is either a field or a polynomial ringF[X] for some field F?