If A is positive definite, every entry along the diagonal of A is positive.

Name: If A is positive definite, every entry along the diagonal of A is positive.
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Question

Quizplus · Accepted Answer

By definition, a matrix A is positive definite if for any non-zero vector x, the quadratic form x^T A x is positive. This implies that all eigenvalues of A are positive, which in turn implies that all diagonal entries of A are positive.

If a Is Positive Definite, Every Entry Along the Diagonal