nomadreid's latest activity

Thanks very much, Gavron! I see my error now. I had not rid myself of my prejudice that isomorphism preserved all structures; I...

The transposition of a complex number is the same complex number, and the conjugation of a real matrix is the same real matrix. It is...

Thanks, Gavran, but apparently I did not express myself very well. Let me try again. First, if I understand your post correctly (but...

The conjugation of a complex number is also a complex number. So the conjugation of a complex number twice corresponds to the...

So, for example, if we take the Hermitian adjoint (the composition of the complex conjugate and the transpose), I would deduce from your...

Thanks, Gavron. These simple examples are very nice.

There is an isomorphism between the field of complex numbers and a specific set of 2x2 real matrices where a complex number ## a+bi ##...

Again, thanks, martinbn. Indeed. I think you mean I oversimplified or neglected the structures that accompany each.

But the usual identification of the complex numbers and the real plane sends ##a+bi## to ##(a,b)##. You are looking at something different.

Thanks very much, martinbn. As fresh_42 pointed out, I was (erroneously) thinking of the real plane along with extra structure...

What do you mean by a matrix in the real plane? The real plane is not the set of such matrices. More importantly why do you expect this...

Interesting! Thank you very much, fresh_42. I will look further into that.

##\mathbb{C}\not\cong\mathbb{R}^2## The complex numbers are a field; the complex plane is not a field. If you want to identify them...

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so...

Thanks, fresh_42!