Search

14 Oct 2015: b. a. a. b. c. ab. abc. bc. L1 S5. What is a vector? ... a. b. L1 S8. Quaternions. Generalises complex numbers, introduced the cross product and some notation still in use today.

14 Oct 2015: L1 S4. Vectors and Vector Spaces. a. b. ab. b. a a. ... product and an area term. a. b. L1 S8. Quaternions. Generalises complex.

22 Feb 2015: Any multiple of ray represents same point. x,y  a,b,c. ... U A A’B’B R. 3D Projective Geometry• Points represented as vectors in 4D• Form the 4D geometric algebra. •

20 Nov 2015: Careful with typographical. ordering. Blade product. L8 S23. bladeprod (a,n) (b,m) = (x,r). ... Blades] [Blades]. AB=simplify([bladeprod(a,b) | a <- A, b <- B]). Form every combination of product.

20 Nov 2015: Careful with typographical ordering. Blade product. L8 S23. bladeprod (a,n) (b,m) = (x,r). ... Blades]. [Blades]. AB=simplify([bladeprod(a,b) | a <- A, b <- B]). Form every combination of product from the two lists.

22 Feb 2015: a  b  I a  b. B  Iaa  IB. ... I(B) is a known linear function of these mapping bivectors to bivectors. •

19 Feb 2015: B = 12 (B BE), EB = B. (4.32). These give rise to the two separate instanton numbers, one for each of the SU(2)subgroups.

14 Feb 2015: Oziewicz, B. Jancewicz, and A. Borowiec,editors, Spinors, Twistors, Clifford Algebras and Quantum Deformations, page233. ... Academic Press Ltd.,London, 1966. 14. [10] B. de Witt. Supermanifolds. Cambridge University Press, 1984.

18 Feb 2015: R(ab) a(b) b(a) (a)(b) (22). and is a linear function mapping bivectors to bivectors. ... R = 2(a(a)) (43). and. G(a) = [(a) a(b(b))]. (44). 6.

19 Feb 2015: a'!)ao ¡ ¡! } m Å b b ¿c b h (Ì / Ê£ÍÏÎÐÉ¡ÊhÑ Ë ÎÐÏ. ... oj! ª M j mh u¤ ª "j b h£¤ b b_ b ¥ o £ ; _K Oo_ª mq £ ¤j J µ ¡ ¥5P ¡ h_º!

16 Feb 2015: R(ab) a(b) b(a) (a)(b). (2.14). From this we define the covariant Riemann tensor. ... R(B) = ḢBetet H2B 14κ2BSS 12κ(BD)S, (3.11). 9. for an arbitrary bivector B.

19 Feb 2015: b a 4.9. a abb aba. 4.10. The multivector analog of complex conjugation is defined by. ... To verify this, consider Holland’s otherchoice:. b b. 4.18. On substituting this into 4.13 we find that.

25 Mar 2015: 2. The bivector B gives us the plane of rotation (cf Lie groups andquaternions). ... where is the relative (3-d) vector derivativeMaxwell’s equations:. E = ρ B = 0.

18 Feb 2015: a) a(b(b)) = M(αann) M a((αn)n αnn) (57). which is also a total divergence and can be converted to a surface integral. ... M ρ3 2π. 0. dφ. dz sin2φ cosφ(iσ3)[i(βσ2n)]. ρ′ρ. d3x ρ′ cosφ(iσ3)[(γ2) γ2(b (b))]. =

18 Feb 2015: R(ab) a(b) b(a) (a)(b). (2.17). From this we define the covariant Riemann tensor. ... The Riemann tensor and its adjoint are related by. R(B) R̄(B) = b[B(aR(ab))] 1.

19 Feb 2015: B»>µ[><><>º9»>9p»>C¿p<Cºi,»CS,ÄáÕ ì>[5»>µ[>9p»>pÉÔÀ¿º|B<>[B>º»PC<>:>ÎC. "# ÿ X À> º|(,ÄpBÆ>º|pÏPµ[,»><p»G:5»>µ[ ... Ê»<>Ä>iº9pBº|µ[iµCB<>º9»>pwpÄà,µ[,Ä>|ºiµCB[ÉSÔ,» mÃp»>CwÄ[<>>5,q,Bĺ9»>àGÆ>ºi

2 Feb 2015: 7. product ab is scalar-valued, since ab ba = (a b)2 a2 b2. ... x b a b|a b| x. a b|a b|b (4). which represents the simple rotation in the ab plane.

19 Feb 2015: dMN>OHRA L]vw?%DBA>@MN>OHRA L ANV9M m<%hR>OHRQDGG>IA B. ( ... DGS $A BIv[]DGSHRFX7;v f v7}Ev B. %. v wxA MTETDXMBH L]W.

16 Feb 2015: Rh1(ab) a(b) b(a) (a)(b). (2.13). The Ricci tensor, Ricci scalar and Einstein tensor are formed from contractions ofthe Riemann tensor:. ... The Riemanntensor for this solution evaluates to. R(B) = M2ω3 (B 3σγBσγ), (4.18).

19 Feb 2015: 2. Euclidean Geometry and Spinors. Let R3 be a three-dimensional Euclidean vector space whose inner product isdenoted by (a,b) 7 ab. ... 2.11) (ba) x(ba)1. = baxa1b1 =baxab. ‖a‖2‖b‖2Let u a/‖a‖, v b/‖b‖ and R vu be the corresponding unit