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Calculate inverse of quaternion


n = quatinv(q)


n = quatinv(q) calculates the inverse, n, for a given quaternion, q. Input q is an m-by-4 matrix containing m quaternions. n returns an m-by-4 matrix of inverses. Each element of q must be a real number. Additionally, q has its scalar number as the first column.

The quaternion has the form of


The quaternion inverse has the form of



Determine the inverse of q = [1 0 1 0]:

qinv = quatinv([1 0 1 0])

qinv =

    0.5000         0   -0.5000         0


[1] Stevens, Brian L., Frank L. Lewis, Aircraft Control and Simulation, Wiley–Interscience, 2nd Edition.

Extended Capabilities

Introduced in R2006b