1.
Norms and Angles
A similar Transformation takes place in the quaternians. ... Given a quaternian over a field that includes all its square roots, divide through by the ...
2.
Inverting a Matrix
This is the second column of R, i.e. M*c gives the second column of the identity matrix. Do this for every column in the identity matrix and build R. ...
3.
Cross Product
Let's try a 3 dimensional example. 3 3 3 7 0 5 ? ? ? Compute the three cofactors and find a cross product of (-15,-6,21). You'll notice that this vector, ...
4.
Normal Vector, Osculating Plane
Paths, Normal Vector, Osculating Plane. Normal Vector, Osculating Plane. Recall our direction vector, d(t), which is velocity divided by speed. ...
5.
Linear Algebra
Linear Algebra, An Introduction. Introduction. A vector space is a left or right unitary module over a division ring or a field. ...
6.
Linear Transformations
Since the image of k times a vector is k times the image of the vector, a linear transformation maps lines to lines in real space. ...
7.
Free Objects
Now let R be another abelian group and let f map {1,2,3} into R. Let g map the 3 generators of Z3 to the same 3 images in R. The rest of g is defined by ...
8.
Polar Coordinates
Math reference, paths in polar coordinates. ... That's fine, but we usually want the velocity expressed in the directions of r and θ, rather than the x and y ... Differentiate again, using the chain rule, to get acceleration. ...
9.
Equivalence Relation
The reciprocols 1/n are not well ordered, because there is no least element. The rationals and reals are not well ordered because they contain the ...
10.
P-adic Numbers
Therefore the partial sums approach each other, and s is convergent. .... represent s give the same result, namely s*t, and multiplication is well defined. ...
