Let ∑ be the variance-covariance matrix of a random vector X. The first component of X is X1, and the second component of X is X2.
<=> the inverse of ∑ does not exist
<=> there exists c≠0 such that
d=(c1)(X1)+(c2)(X2) (i.e. (c1)(X1)+(c2)(X2) is equal to some constant d almost surely)
I don't understand the last part. Why is it true? How can we prove it?
Any help is appreciated!
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