Quaternion Function Reference

log

Natural logarithm
(Quaternion overloading of standard MATLAB® function)

Syntax

Y = log(X)

Description

log(X) computes the natural logarithm of the elements of the quaternion array X.

The logarithm of a quaternion is not difficult to derive, as follows. First note that exp(y) = x (definition of logarithm). Then write x in polar form as r × exp(μθ). Then we have: ln(x) = y = ln(r) + ln(exp(μθ)) = ln(r) + μθ. Note that r and θ may be complex if X is a complex quaternion.

Examples

>> log(quaternion(1,1,1))

ans = 0.5493 + 0.9069 * I + 0.9069 * J + 0.9069 * K 

See Also

QTFM function: exp
MATLAB® function: log

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

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