Commutation (e.g. the trivector imaginary commutes)

Com3[A_, B_] := Mul3[A, B] - Mul3[B, A]

Com3[i3, a3v]//MatrixForm (* i3 commutes with vectors *)

( {{0}, {{0, 0, 0}}, {{0, 0, 0}}, {0}} )

AntiCom3[A_, B_] := Mul3[A, B] + Mul3[B, A]

AntiCom3[i3, a3v]//MatrixForm

( {{0}, {{0, 0, 0}}, {{2 ax, 2 ay, 2 az}}, {0}} )

Com3[σix, a3v]//MatrixForm (* ... but bivector imaginaries in 3 - space do neither ? *)

( {{0}, {{0, 2 az, -2 ay}}, {{0, 0, 0}}, {0}} )

AntiCom3[σix, a3v]//MatrixForm

( {{0}, {{0, 0, 0}}, {{0, 0, 0}}, {2 ax}} )

Created by Mathematica  (April 17, 2005) Valid XHTML 1.1!