Talk:Elements of Dynamic

Missing minus sign

Clifford representation of split-quaternions, page 171 of Elements of Dynamic:

• 1 = (1,0,0,1) leaves figure unaltered,
• I = (1,0,0,-1) turns it over about oY
• J = (0,1,1,0) interchanges oX an oY
• K= (0,1,-1,0) turns counterclockwise through a right angle.

Stated consequences: $I^{2}=1,\ \ J^{2}=1,\ \ K^{2}=-1,\ \ JK=I=-KJ,\ \ KI=J=-IK,\ \ IJ=K=-JI$

• Missing minus sign, should be JK = −I.

The error may have been a typographical slip-up, perhaps with a typesetter "who knew how vectors multiply". Indeed, the in the quaternion group there is no minus sign. This glilch, at the dawn of linear algebra, was problematic. In 1893 Knott showed that the positive squares were impossible when multiplication is associative and i, j, and k multiply as in the quaternion group. See hyperbolic quaternion. Rgdboer (talk) 22:52, 28 August 2026 (UTC)