Norm

The algebra norm of a hypercomplex element: the determinant of multiplication-by- on the -dimensional space. Reduces to the Gaussian at one imaginary unit.

WikipediaNorm (mathematics)↗MathWorldNorm↗WikidataQ956437↗Encyclopedia of Mathematicsnorm↗Britannicatopic/norm-mathematics↗

Norm(z)the determinant of the multiplication-by- map

Domain: Hypercomplex algebra

Details

• Computed through the tower : for , , bottoming out at a scalar
• NOT — the signature is mixed, and at that product keeps a live part
• Multiplicative on a FIXED unit set; the norm is taken over the subalgebra generated by the units occurring in , and adjoining a generator squares it
• is invertible exactly when its norm is; a norm of marks a zero divisor
• Left symbolic for the anticommuting families, whose norm is a different object

Examples

See also: Conjugate, NonCommutativeMultiply, Basis