Recent content by daveyp225

But they do not travel at, say, (1-10^(-200))*c.

And what might the aftermath be of the expected (non-elastic) collision? It's hard to imagine a proton could do much? That is my motivation for this question

For the sake of argument, say an proton traveling at near light-speed having momentum far exceeding the Earth's were to collide with Earth head on. What would happen in this case? Would the result be any different replacing the proton with a small asteroid of the same momentum? Is it possible...

Introduce them to the Hill Cipher

An R-Algebra is an R-module closed under some multiplication operation. i.e., an R-module that is also a ring. For a special (associative) case, the set of n x n matrices with entries from a ring R is a dimension n^2 R-module closed under the usual matrix multiplication.

The triangle's height is not 2.

Thanks for the suggestion. I have to erase a board probably 10 times a lecture, so wiping it down with water will not work well for me.

In the following MIT video, some kind of thick chalk (not sidewalk, already tried it) is used in the lecture: http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/lecture-2-limits/ It looks like great chalk. Or what chalk is this easy to write with?

Elementary matrices represent row operations on a matrix. For example, given: A=\pmatrix{1 & 2\\-2 &1} Adding 2 times row 1 to row 2 is the same as multiplying A on the left by: E_1 = \pmatrix{1 & 0\\2 & 1} We get \pmatrix{1 & 0\\2 &1}\pmatrix{1 & 2\\-2 &1} = \pmatrix{1 & 2\\0 &5}...

It is a question in a linear algebra book which states that linear functionals on a subspace of F^n (the subspace which consists of all vectors whose components sum to 0) can be identified with linear functionals whose coefficients sum to 0. I understand the "identification" part, it is obvious...

What does it mean for a space to be "naturally identified" with another? Does it mean there is a bijection? Or maybe an isomorphism?

I got a little ahead of myself here. It took me some to see the "obvious" fact that if a semidirect product is abelian then it is only a direct product, which happen if the only automorphism is the trivial one. Something I wish was written down somewhere. Though I wonder if all groups which can...

I would have to agree with you. Though, you can define an inner product on m x n matrices by adding the products of the corresponding entries in the matrices. It ends up being the same as the standard dot product on vectors in R^mn.

It depends on how the 'dot' has been defined. In this case it is the product of M with itself so i suspect it just gave the formula for M^2. However, it is not a "dot product". Dot products -- more generally inner products -- give back a number.

That is the product M*M=M^2. When you multiply two matrices, the product will have in its ith row and jth column the dot product of the ith row of the left matrix times the jth column of the right matrix. So to get the first entry (entry in the first row, first column), you perform the dot...