What is a positive definite matrix? What are the properties of a positive definite matrix? If a is a positive definite matrix, then a [i] [i] must be greater than 0?

For symmetric matrix A, if x * ax > 0 holds for any nonzero vector x, then a is positive definite
If a is a positive definite matrix, then a [i] [i] must be greater than 0, because a [i] [i] = EI * AEI > 0
Where EI is the ith unit vector

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