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Group Theory and Linear Algebra Thread

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kamil9876:
mod 8:

:0 1 2 3 4 5 6 7

:0 1 4 1 0 1 4 1

(notice how it is symmetrical since , saves you half the time)

so amongst you cannot have no 4 or just a single 4 since otherwise the sum would be too small. So you need at least two 4's. But two 4's is 0 so that also makes your sum too small.

pooshwaltzer:
Please suggest a possible financial application for said theory. Thanks.

QuantumJG:

--- Quote from: kamil9876 on August 21, 2010, 06:20:48 pm ---mod 8:

:0 1 2 3 4 5 6 7

:0 1 4 1 0 1 4 1

(notice how it is symmetrical since , saves you half the time)

so amongst you cannot have no 4 or just a single 4 since otherwise the sum would be too small. So you need at least two 4's. But two 4's is 0 so that also makes your sum too small.

--- End quote ---

Thanks Kamil. There was a question earlier where we had to do a multiplication table for 8 and I noticed that symmetry.

QuantumJG:
This is a problem from last years exam.

Let V = and T: V V be the linear transformation defined as:

T(p(x)) = p(x+1) + 3p'(x)

a) Find the matrix T with respect to the basis {} for V.

So I got:

p(1) = {1,0,0}
p(x) = {2,1,0}
p(x2) = {1,4,1}

So I got T to be:



I just want to make sure this is right!

kamil9876:
you want to be finding . I have no idea what you mean by etc., typo?

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