Example of Quaternions

Matrix Theory: For the quaternion alpha = 1 - i + j - k, find the norm N(alpha) and alpha^{-1}. Then write alpha as a product of a length and a direction.

Category:

Education

Tags:

• Mathematics
• matrix
• theory
• linear
• algebra
• quaternion
• conjugate
• unit
• vector
• norm
• inverse

[Trotskisty]

What's with the big stick..?

[MathDoctorBob]

@Trotskisty Old sparring stick, but I use something more pointer-like these days. - Bob

[MathDoctorBob]

@Trotskisty Old sparring stick. I've upgraded to a regular pointer. - Bob

[odinheim]

sorry were you doing the dot product at 4:50 on the video ? alpha*alpha^-1 ?

[MathDoctorBob]

@odinheim The last board is quaternion multiplication - the whole i.j = k business. I check that alpha*alpha^{-1} = 1 because I need to give an example of multiplication with linear combinations.

At some point, I'll do more with H and make the connection to the dot and cross products on R^3 explicit.

[ryanmichaelhaley]

Check out Second Life. You can write some quick scripts that illustrate the rotational vector as you rotate an object, and simultaneously display the quaternions. It's a useful (and free) program for studying vectors, physics, and quaternions. It's where I do all of my playing. Look me up, my in-world name is Dragon Niu.

[odinheim]

@MathDoctorBob Hey , thanks for replying I wonder if I can watch some animation of the quaternions functions , polynomials with complex numbers ,

[odinheim]

This is very interesting stuff , Quaternion algebra was introduced by Irish mathematician Sir William Rowan Hamilton , at his time it was a revolution , excellent video