Recent content by mitch_jacky

Wow, it isn't wizard math after all. Thanks man!

You know, I think that's pretty much what I am being asked to show. I appreciate your insights! So basically (and please excuse the poor notation, I'm on my phone): (H,\otimes,°,\oplus, =)~(M, ×, •, +, =)

Okay, so an isomorphism is a bijectivity from one structure to another which preserves the characteristics of the structures. So if quaternions possesses addition, scalar and quaternion multiplication I must show that this structure is isomorphic to the addition, scalar, and matrix...

The more I look at this problem the less I understand what I am supposed to be doing. Without giving me any answers what I need is for someone to walk me through the steps to the solution. I need an understanding of what I'm trying to solve here.

Okay, I have verified that ij=k but I don't see what to do next.

I just started learning about morphisms and I came across a problem that totally stumps me. Here goes: Show that the algebra of quaternions is isomorphic to the algebra of matrices of the form: \begin{pmatrix} \alpha & \beta \\ -\bar{\beta} & \bar{\alpha} \end{pmatrix} where α,β\inℂ...

Thanks, I figured it out a little while afterwards and lost my internet connection.

Nope, still got nothing. I still can't figure it out.

Ah, thanks a ton!

Arc length of y=ln((e^(x)+1)/(e^(x)-1)) on [a,b] Using L=\int\sqrt{1+(y')^2}dx on [a,b] I am having difficulties differentiating y and plugging the results back into get a useful integral. So far I have y'=2e^(x)/(e^(2x)-1)