Question

A is positive definite if and only if a inverse is positive definite

Answer 1

if its eigenvalues are allpositive. Thus, since is positive-definite, the matrix does not have as an eigenvalue.

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Answer 2

Answer:

Recall that a symmetric matrix is positive-definite if and only if its eigenvalues are all positive. Thus, since A is positive-definite, the matrix does not have 0 as an eigenvalue. Hence A is invertible.

Step-by-step explanation: