Recent content by nomadreid

Thanks very much, Gavron! I see my error now. I had not rid myself of my prejudice that isomorphism preserved all structures; I understand now that isomorphism only preserves the specific operations that define the structure in question, but that "transpose" is an additional structure...

Thanks, Gavran, but apparently I did not express myself very well. Let me try again. First, if I understand your post correctly (but probably I am not), it seems that in Post #8, that you are stating Then, however, suppose we take the complex conjugate of both sides , then we get where α† is...

So, for example, if we take the Hermitian adjoint (the composition of the complex conjugate and the transpose), I would deduce from your sentence that this would mean that the conjugation of the conjugate of scalar s corresponds to the Hermitian adjoint of its matrix representation; that is, s...

Thanks, Gavron. These simple examples are very nice.

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

Thanks very much, martinbn. As fresh_42 pointed out, I was (erroneously) thinking of the real plane along with extra structure, i.e., perhaps as a part of ℝ4, and also as fresh_42 pointed out, there isn't the isomorphism which secondary school introductions to the complex plane give the...

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

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other...

Thanks, fresh_42!

Thanks, fresh_42. I know that it's pure convention, but I am trying to understand the relations between the conventions. What is clear is that ---physicists often use bra-ket <v|u>, linear in the second argument and ---mathematicians often use (u,v) , linear in the first argument, What is...

anuttarasammyak, thank you for pointing out that I should have made precise that I was referring to complex vector spaces. I have edited the question accordingly. However, the question still stands.

First, I need to check that I have the 3 notations correct for an inner product in finite vector spaces over a complex field; v* means: given the isomorphism V to V* then: (a) physicists and others: (u,v)=v*u ; linear in the second argument (b) some mathematicians: (u,v)=u*v; linear...

Thanks very much, PeterDonis. Hm, Indeed I appear to have read it too quickly, having been led astray by the summary by the journal at the beginning (which deceptively makes it sound as if there was a quantum aspect to the experiment), but I see from the quote by the author that “Since we...

I am not sure if this belongs in the biology section, but it appears more of a quantum physics question. Mike Wiest, Associate Professor of Neuroscience at Wellesley College in the US. In 2024 he published the results of an experiment on anaesthesia which purported to point to a role of...

The following is more or less taken from page 6 of C. Smorynski's "Self-Reference and Modal Logic". (Springer, 1985) (I couldn't get raised brackets to indicate codification (Gödel numbering), so I use a box. The overline is assigning a name. The detail I would like clarification on is in...