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comment Can one branch of mathematics be completely learned from the perspective of another branch of mathematics?
The question atleast makes sense in the context of drawing analogies to prove theorems, may be across branches. The following quote may throw some light: "A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies."-Stefan Banach
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answered Why is symplectic geometry so important in modern PDE ?
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accepted Optimization version of the Sylvester equation
Dec
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comment The distribution of roots of elliptic polynomial
I think G.B.Folland discusses this in his Introductory book on PDE.
Dec
27
comment Optimization version of the Sylvester equation
@Suvrit Thank you for the answer. Your answer settles the fact that there exists a solution. But, my original interest, which I unfortunately did not make it clear in my post, is to get some quantitative information on the bounds of the solution w.r.t the eigenvalues of $A$ and $B$.
Dec
27
comment Triangularizing a function matrix with smooth eigenvlaues
I have figured out a way to translate the paper. Thank you once again.
Dec
27
comment Optimization version of the Sylvester equation
@Igor Khavkine Yes, my interest is in the case when the matrices have overlapping spectra. I have edited the question to reflect this.
Dec
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revised Optimization version of the Sylvester equation
added 162 characters in body
Dec
27
comment Optimization version of the Sylvester equation
Thank you for the reference.
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asked Optimization version of the Sylvester equation
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12
comment Triangularizing a function matrix with smooth eigenvlaues
@András Bátkai Thank you for the reference. I will try to get this paper. Is there an English translation of this paper?
Dec
12
comment Triangularizing a function matrix with smooth eigenvlaues
@Denis Serre Yes. Kato's book discusses Jordan form. But, I find that questions about Jordan form and triangular form are a bit different. For example, the matrix $$ \left(\begin{array}{cc} 1&z\\ 0&1 \end{array}\right) $$ is trivially triangulariable with smooth entries but cannot be written in Jordan form at $z=0$.