Timeline for Imaginary eigenvalues
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 4, 2021 at 14:35 | vote | accept | Pritam Bemis | ||
| May 27, 2021 at 6:36 | comment | added | Carlo Beenakker |
the Mathematica command for matrix multiplication is Dot --- so to multiply a list of matrices $A_1,A_2,A_3,\ldots A_n$ you could enter Dot@@Table[A[i],{i,1,n}]
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| May 26, 2021 at 22:58 | comment | added | LSpice |
@მამუკაჯიბლაძე, re, in so many other respects Mathematica often DWYM (for example, it's perfectly happy to do the multiplication {{a, b}, {c, d}}.{x, y} without requiring, as it technically should, that you transpose it {x, y}.Transpose[{{a, b}, {c, d}}]), but the decision to make the default way of multiplying matrices be entrywise is surely a wart.
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| May 26, 2021 at 21:10 | comment | added | Antoine Labelle | Another quite surprising property is that the characteristic polynomial is symmetric in the $\mu_i$, that is, the eigenvalues are independent of the order in which the multiplication is done. I wonder what explains that. | |
| May 26, 2021 at 19:02 | history | became hot network question | |||
| May 26, 2021 at 14:47 | comment | added | Antoine Labelle | Hahaha ok that explains it. Using sage I got, for $n=3$, $k_1^2k_2^2k_3^2+\sum_{sym} (k_1^2k_2^2 +2k_1^2k_2k_3+4k_1^2+4k_1k_2) +18$ for the coefficient of $t^2$ | |
| May 26, 2021 at 14:46 | comment | added | მამუკა ჯიბლაძე | Sorry my first comment is complete rubbish | |
| May 26, 2021 at 14:44 | comment | added | მამუკა ჯიბლაძე | @AntoineLabelle OMG it seems I have a bug! I multiplied the matrices entrywise!! | |
| May 26, 2021 at 14:42 | comment | added | მამუკა ჯიბლაძე | Well unless Mathematica has a bug... :) | |
| May 26, 2021 at 14:40 | comment | added | Antoine Labelle | @მამუკაჯიბლაძე Are you sure? I computed it for $n=3$ and got something completely different (the coefficient of $t^2$ is a messy polynomial in $\mu_1, \mu_2, \mu_3$) | |
| May 26, 2021 at 13:50 | comment | added | მამუკა ჯიბლაძე | Characteristic polynomial for odd $n$ is$$1+(3+\prod_{i=1}^n\mu_i^2)t^2+t^4$$ | |
| May 26, 2021 at 13:44 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
mystical --> imaginary
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| May 26, 2021 at 11:32 | answer | added | Carlo Beenakker | timeline score: 15 | |
| May 26, 2021 at 11:02 | history | asked | Pritam Bemis | CC BY-SA 4.0 |