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14 Oct 2015: chrisjldoran. #geometricalgebra. github.com/ga. L1 S3. Some history. William Hamilton Hermann Grassmann William Clifford. ... numbers, introduced. the cross product and. some notation still in. use today.

14 Oct 2015: cjld1@cam.ac.uk. @chrisjldoran. #geometricalgebra. github.com/ga. L1 S3. Some history. William Hamilton. Hermann Grassmann. ... a. b. L1 S8. Quaternions. Generalises complex numbers, introduced the cross product and some notation still in use today.

18 Feb 2015: Thislanguage includes a calculus which goes some way beyond what is available inalternative languages. ... After some rearrangement this can be brought to the form. R4(B) = 14 ab (al)lBl(bl) 14 (al)(bl) alBlb.

19 Feb 2015: it. is somewhat simple to show that, for some bivector B, where B2 = 1, the locusof the action of exp(B φ2 ) upon a point with respect to varying φ is ... if n A(m 1, 1) then {a, b, c} Rm. It is clear that the set of allB is some linear subspace of all

25 Mar 2015: Some History. Hamilton (1840s): 3Drotations via quaternions. Grassmann (1870s): exterior(wedge) product; orientedobjects. ... Some consequences of this view — though starting from the Bohmian interpretationof non-relativistic quantum mechanics — have

18 Feb 2015: endpoint of rotating, collapsing matter. Some implications of these results. for physically-realistic black holes are discussed. ... Some further insight into the nature of the solution and the role of thecomplex structure is obtained from the form of

18 Feb 2015: This should be con-trasted with the gauge-dependent temperature perturbation used by some authors(see Section 5 for examples). ... Q(k)a Sk(3)aQ(k), Q(k)ab S. 2. k2(3)(a(3)b)Q(k) 13 habQ. (k).(2.28). Some useful properties of the scalar harmonics

14 Feb 2015: All matter fields are now parameterised by avector variable x, but in so doing are we not returning to some Newtonian notionof an absolute space? ... In doing so we lose some of the information contained in the ‘wedge’ equation (11).This information

16 Feb 2015: theform of closed timelike loops (CTL), and has prompted much discussion on thepossibility of building a time machine from some system of rotating cylinders. ... t′ = At Bφ. φ′ = Ct Dφ(2.135). for some real constants A, B, C, and D.

18 Feb 2015: A The Dirac operator algebra 101. B Some results in multivector calculus 102. ... A(BC) B(CA) C(AB) = 0. (2.18). Finally we introduce some further conventions.

14 Feb 2015: To my parents. Contents. 1 Introduction 11.1 Some History and Recent Developments. ... 422.2.2 Example II. The Grassmann Fourier Transform. 44. 2.3 Some Further Developments.