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 Oct 2 comment Tensor product of operators Should not the last expression be of the similar form as for vectors, i.e. $T=\sum_i \sum_j c_{ij} T_{1,i} \otimes T_{2,j}$? Dec 1 comment Inner product for vector space over arbitrary field Hmmm... I think the requirement that the field should be ordered is a bit too strict and it obviously won't even work for complex vector spaces. A presence of an ordered subfield in the field should be enough as in the case of a complex vector space, where the inner product is defined in such a way that it always returns the value from the field of real numbers (which is an ordered subfield of the field of complex numbers) when both arguments are the same. Nov 15 comment What is the null vector for the vector space of continuous functions $f \colon \mathbf{R} \to \mathbf{C}$? Just a quick follow-up that came into my head right now: strictly speaking is it also true for $L^2$? Or there is something funny with the "Lebesgue measure zero" as in the case of the equivalence of two functions? I don't know what this "Lebesgue measure zero" actually is, but I just read that two functions on $L^2$ are considered to be equivalent if the are equal everywhere except on a subset of the real numbers that have this "Lebesgue measure zero" (whatever it is). Jun 3 comment Distinguishing between symmetric, Hermitian and self-adjoint operators @leslietownes thanks for the reference! ;) So it was Friedrichs who met Heisenberg, not von Neumann himself, and this story is not an anecdote. Jun 3 comment Distinguishing between symmetric, Hermitian and self-adjoint operators Hmmm... Self-adjoint implies symmetric by definition. But how do we know that Hermitian implies self-adjoint? Apr 23 comment Is there any standard notation for specifying dimension of a matrix after the matrix symbol? @Arkamis Of course. That's how we use parentheses to resolve ambiguities. You're right. Thanks. :) Apr 23 comment Is there any standard notation for specifying dimension of a matrix after the matrix symbol? @Arkamis But I want to specify the dimension of conjugate transpose matrix, not the initial matrix. Apr 23 comment Is there any standard notation for specifying dimension of a matrix after the matrix symbol? @Arkamis This notation can be ambiguous. I've updated my question to show a specific example when this is the case. Mar 1 comment What's the difference between tuples and sequences? This caught us by surprise today. There are no strict defenitions? :O Really? Usually, by convention. Sounds weird for mathematics. Seems like we just have two terms for one thing and a convention... Occam's razor to the rescue! Feb 6 comment Is such integration by parts with $u = \frac{f\left( x \right)}{dx}$ valid? Oops! Need to sleep more. :D It's just a definition of this rule... Well, actually even with my plain stupid substitution I can end up with the same result. The mistake is in du and v. du = df(x)/dx and v = g(x)dx.