Norm of an octonion
Y = normo(X)
(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.
normo(octonion(1,1,1,1,1,1,1,1)) ans = 8normo 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