Quaternion Function Reference

normo

Norm of an octonion

Syntax

Y = normo(X)

Description

(Not to be confused with the function norm which computes a matrix norm.)

normo(X) returns an array Y such that each element of Y is the norm of the corresponding element of X. The norm is the sum of the squares of the eight components (seven components in the case where X is pure).

If X is a complex octonion, normq(X) returns the complex semi-norm, computed in the same way. The semi-norm of a complexified octonion can vanish. See the QTFM function normq for references on this topic for quaternions. No corresponding paper is known for the octonion case.

Examples

normo(octonion(1,1,1,1,1,1,1,1))

ans = 8
normo is vectorized, and hence can operate on arrays. It can also operate on complex octonions yielding a complex result in general (the semi-norm):
>> normo(1 + i + oi + on + om)

ans = 3.0000 + 2.0000i

See Also

QTFM functions: abs, norm

© 2008-2013 Stephen J. Sangwine and Nicolas Le Bihan

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