Cookie Thread Act 7: Romulus

literally Narcissa Squilliams

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:x:

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the initial for the discord would be A, because A is better than B

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fuck that goes hard

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me personally S1E3 is my favorite
otherwise ur rankings are pretty good, assuming ur not saying that these episodes are bad just better than others

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No

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:ballot_box_with_check:

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I must apologise. This is outside my MENTAL realm

saying this anytime anyone asks me something i dont know

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I don’t think Arcane has any bad episodes: S1E2’s just meh because it’s both setting up a bunch of stuff and just repeating a lot of S1E1.

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similarity is determined not by characteristic and minimal polynomials, but by the Jordan Canonical Form. A matrix with char. poly (x - 3)^4 and min. poly. (x - 3)^2 has two possible Jordan Forms, one with 2 2x2 Jordan blocks and one with 1 2x2 and 2 1x1 Jordan blocks. matrices of these two forms are not similar to each other

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you’re all learning so much today

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Yep.
Learning a lot about how the mute function works.

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so you see the reason why we dont really learn anything is that i have no clue whats the building blocks of that question

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this court finds you guilty of anti-cookie thread activity and orders you to be shot

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inner product spaces might be more up your alley. it’s just a generalization of the dot product

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wait but how can the geometric multiplicity of the eigenvalue influence the structure of the Jordan Canonical Form in this case, and how does it relate to the number of Jordan blocks for a given eigenvalue???

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jordan peterson?

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that’s a good question! The number of Jordan blocks for a given eigenvalue is actually equivalent to the number of eigenvectors for that eigenvalue. while this is often the multiplicity, you do have to take into account that the matrix could be defective, and therefore have fewer eigenvectors for a given eigenvalue than its multiplicity.

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This is to say, the JCF gives us information about how many total eigenvectors there are (so the first case in that problem there are 2 eigenvectors for the eigenvalue 3, and in the second case there are 3). either way, the matrix is defective, because 3 is the only eigenvalue, with multiplicity 4.

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