Just to make sure that I'm getting this, the bottom expression isn't actually subtracting a scalar from a vector, it's keeping them as seperate coordinates right?
ngandhi
^^ I'm confused about this too
dranzer
Yes, u * v have the components of i, j and k. Therefore this is just a simple representation of a quarternion in terms of dot products and cross products. You can also see this from, the above expression by putting in a=0, b=0. We just wrote it all in a single form rather than a (scalar, vector) form.
atarng
Does it make sense to think of a quaternion like a 4D vector (like thinking of a complex number as a 2D vector)? I'm confused about the role of the "scalar" term
peanut
^^ Confused about scalar, too. Can we think it as a magnitude? Or norm?
Just to make sure that I'm getting this, the bottom expression isn't actually subtracting a scalar from a vector, it's keeping them as seperate coordinates right?
^^ I'm confused about this too
Yes, u * v have the components of i, j and k. Therefore this is just a simple representation of a quarternion in terms of dot products and cross products. You can also see this from, the above expression by putting in a=0, b=0. We just wrote it all in a single form rather than a (scalar, vector) form.
Does it make sense to think of a quaternion like a 4D vector (like thinking of a complex number as a 2D vector)? I'm confused about the role of the "scalar" term
^^ Confused about scalar, too. Can we think it as a magnitude? Or norm?
Do we need to memorize all of these for exam?