Inverse QuaternionsDate: 12/01/1999 at 06:09:16 From: Jarno Kuoppamaki Subject: Inverse Quaternions How do you calculate inverse quaternions? For example, the inverse of 3 - 4i + 5j + 6k. Date: 12/01/1999 at 12:27:40 From: Doctor Rob Subject: Re: Inverse Quaternions Thanks for writing to Ask Dr. Math, Jarno. Call a = 3 - 4*i + 5*j + 6*k. Write the inverse in the form 1/a. Multiply the numerator and denominator by a with -i substituted for i, -j substituted for j, and -k substituted for k, or 3 + 4*i - 5*j - 6*k Expand and simplify the denominator, which should result in a real number, 86 in this case: 86 = 3^2 + (-4)^2 + 5^2 + 6^2 Divide that real denominator into each coefficient in the numerator. Result: 1/a = 3/86 + (4/86)*i - (5/86)*j - (6/86)*k - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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