Linear Algebra - LU Factorization

Thread starter ashah99
Start date Jul 14, 2021
Tags

Algebra Factorization Linear Linear algebra Proof

Jul 14, 2021

ashah99

Homework Statement: Please see attached photo for problem statement.

Relevant Equations: LU Factorization concepts

Hello all, I have a problem related to LU Factorization with my work following it. Would anyone be willing to provide feedback on if my work is a correct approach/answer and help if it needs more work? Thanks in advance.

Problem:

Work:

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Sep 24, 2021

benorin

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Thread 'Complex Numbers (Laurent Series)'

see attached.

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Thread 'Necessary criterion for expressing f(a + b)'

It's easy to see that any polynomial is function of that class. Also it seems that composition of exponent and polynomial is good as well. G_f(a, b) should be equal G_f(b, a) as the f(a+b) is symmetrical. Does anyone have information about this or at least related to it?

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Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...

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