Tom
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Registered User
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I'm interested in modular forms and complex geometry
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May 15 |
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Solve for $A$ and $B$ in $AXB=Y$ @ Peter. I was never claiming that I could solve the actual question. In fact, I stated that I can't. I said in the second line that I can give a linear polynomial (in an answer as I haven't got enough rep for commenting) and was then asked to elaborate which I did. |
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May 14 |
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Solve for $A$ and $B$ in $AXB=Y$ I guess we are not on the same page. But, if I take $X$ to be a non-zero number -denoted by $x$- and $Y$ to be $x \cdot I_n$, then there is a solution, although $x$ has rank 1 and $Y$ rank n. Indeed, denoting by $e_i$ the i-th basis vector we have $$Y=\sum_i e_i \cdot x \cdot e_i^t=\sum_i x \cdot e_i \cdot e_i^t.$$ I hope haven't made new mistakes now. |
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May 14 |
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Solve for $A$ and $B$ in $AXB=Y$ I have to admit that I am puzzled now. Peter, could you be so kind to give a short example ? Furthermore, wouldn't that make your comment the desired answer ? btw I just clarified the notation above. |
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May 14 |
revised |
Solve for $A$ and $B$ in $AXB=Y$ clarified what x_{ij} means |
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May 13 |
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Solve for $A$ and $B$ in $AXB=Y$ thanks for editing, Emil ! |
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May 13 |
revised |
Solve for $A$ and $B$ in $AXB=Y$ I elaborated as asked for |
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May 9 |
answered | Solve for $A$ and $B$ in $AXB=Y$ |
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Apr 5 |
answered | Interesting applications (in pure mathematics) of first-year calculus |
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Apr 2 |
answered | Reference on generators of subgroups of symplectic groups |
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Mar 11 |
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Reference on generators of subgroups of symplectic groups Dear Aakumadula, thanks for helping with the syntax! Sorry, I haven't had time to look up your reference in detail, yet ! Dear Nathan, that's a really nice one ! But doesn't $u(1)$ generate all $u(x)$s ? And can't we pick only finitely many $C(a,b,c,d)$s as $\Gamma_0^{(1)}(N)$ is finitely generated ? |
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Mar 5 |
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Reference on generators of subgroups of symplectic groups Indeed, Mumford gives generators for $\Gamma_g$,$\Gamma_g[2]$ and $\Gamma_g[1,2]$ on pages 202-210. But to be honest I was hoping for more. |
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Mar 5 |
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Reference on generators of subgroups of symplectic groups Dear J, as you proposed I just clarified the notation $M=(A B \\ C D)$. With the few generators I was tkinking of E. Freitag 'Siegelsche Modulformen' (in Springer's Comprehensive Studies 254 ) appendix V pages 322-328. The proof relies on the fact that he finds for an EUCLIDEAN ring 'smaller' or 'easier to handle' sets of generators for $SL(g,R)$ and $GL(g,R)$. Now I'm having a look in the 2 books you mentioned. |
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Mar 5 |
awarded | ● Editor |
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Mar 5 |
revised |
Reference on generators of subgroups of symplectic groups added notation $M=(A B \\ C D)$ |
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Mar 5 |
asked | Reference on generators of subgroups of symplectic groups |
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Jan 21 |
awarded | ● Enthusiast |
