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(a) What is the implication of a correlation matrix not being positive-semidefinite? (b) Why are the diagonal elements of a correlation matrix always 1? (c)

(a) What is the implication of a correlation matrix not being positive-semidefinite?

(b) Why are the diagonal elements of a correlation matrix always 1?

(c) Making small changes to a positive-semidefinite matrix with 100 variables will have no effect on the matrix. Explain this statement?

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