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Dec
15
comment How do I know that an inverse of a matrix has the same type of Jordan canonical form
Consider an upper-triangular matrix $A=(a_{ij})$ of the form: $a_{ii}=\lambda$, and $a_{i,i+1}\neq0$ for any $i$. What's the Jordan normal form for $A$?
Dec
15
asked Extending Morse-Smale pair from submanifolds?
Dec
8
comment Affine geometry book for physicist
I hope Shafarevich & Remizov's Linear Algebra and Geometry is a good choice.
Dec
8
revised What are Goldbach conjecture for other algebra structures, matrix, polynomial, algebraic number, etc?
Fix for the URI for the paper
Dec
6
comment What exactly are the elements of a local homology group?
Could you think of simplicial homology? A ref: Seifert & Threlfall.
Dec
6
comment Let $f$ be integrable over $\mathbb{R}$. Show that the following four assertions are equivalent:
I don't understand your proof for (4)$\implies$(1). In fact, if $f>0$ on $E$ where $m(E)>0$, you need to approximate $\int_Ef$ with some $\int_{\mathcal O}f$.
Dec
6
comment Closed set in normed vector space
en.wikipedia.org/wiki/Sequential_space
Dec
6
comment Proving the Leray-Hirsch theorem using the Serre spectral sequence
I don't know whether it's related: On Hirzebruch's Topological Methods in Algebraic Geometry, there's a construction of splitting manifolds which is essentially relied on Leray-Hirsch theorem. His reference is: Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de LIE compacts. Ann. Math. 57 115-207 (1953)
Dec
3
comment Effective Methods of Studying in different areas of Math
It's hard to gauge, and you need to furnish more info about what kind of exercises you're referring to and what's mainly taught in your class. However, anyway doing exercises is an important part of learning mathematics, and you need to know how to do things.
Dec
1
comment How to determine if 2 points are on opposite sides of a line
@martycohen Defined for an arbitrary embedding $\mathbb R^2\hookrightarrow\mathbb R^3$.
Nov
30
comment Prove that $\frac{1}{2\pi}\int_0^{2\pi}|p(e^{i\theta})|^2\,d\theta=\sum_{n=0}^N|a_n|^2.$
Parseval's identity
Nov
29
comment Understanding Bell's inequality vs. quantum mechanics
Let us continue this discussion in chat.
Nov
29
comment Understanding Bell's inequality vs. quantum mechanics
So $A,B,H$ etc you are describing a theory which is incompatible with quantum mechanics? It seems too generalized to me and I didn't understand how my specific example sketched in the question satisfies these things, especially how locality is described in your formalism.
Nov
29
comment Understanding Bell's inequality vs. quantum mechanics
So as a consequence, roughly speaking, we cannot use the same random variable for these two appearances of $a$, say, just like in the Bell's inequality, two appearances of $X$?
Nov
29
comment Understanding Bell's inequality vs. quantum mechanics
Thanks. I've edited the original post substantially (to clarify the question, but what you answer is to the point, except that I cannot fully understand). Could you elaborate the concept of locality with explanation related to the spin measurement just given in the question? (I cannot really understand formulations like each end of the experiment, and for locality, like info propagates at most light-speed, etc. I hope that there's mathematical formulation for this)
Nov
29
comment Understanding Bell's inequality vs. quantum mechanics
I've edited the post substantially. Hope it's clearer now.
Nov
29
revised Understanding Bell's inequality vs. quantum mechanics
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Nov
29
revised Understanding Bell's inequality vs. quantum mechanics
added 45 characters in body
Nov
29
revised Understanding Bell's inequality vs. quantum mechanics
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Nov
29
revised Understanding Bell's inequality vs. quantum mechanics
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