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# Matrices, Eigenvectors, Eigenvalues and Inverses

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Determining the equation for a matrix and confirming the inverse, eigenvalues
Details:
I have think the answer to question (a) is theta^2 [(1-p)I + pJ]. But when I am multiplying the sigma and the sigma inverse I still have "stuff" at the tail end of the identity......being added. I know I should be left with the identity if the two pieces are the inverses to each other.

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Matrices, Eigenvectors, Eigenvalues and Inverses are investigated.

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The attached document gives an explanation of the inverse verification, and demonstrates the eigenvalues and eigenvectors for sigma.

Part (a)

To show that is the inverse, we will verify that:

We can consider first the diagonal entries and off-diagonal entries separately. If we can prove that:

(1) all diagonal entries in the resulting matrix are 1.
(2) all off-diagonal entries in the resulting matrix are 0.

We will have shown that .

(1) Diagonal entries in the above matrix have the form:

This verifies that all the diagonal entries are indeed 1.

(2) The ...

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