Give an example of a square matrix A such that all the diagonal entries are positive...

Give an example of a square matrix A such that all the diagonal entries are positive but A is not positive definite

Solutions

Expert Solution

lets a matrix A = 1 2 3
2 5 4
3 4 9

Here all diagonal entries are positive.

and let check positive definite or not.

Method :1

Check the determinants of all upper- left submatrices are positive or not.

Method :2.

If A matrix is positive definite if it's symmetric and all its eigenvalues are positive.

From both the method we get to know that That given A is not positive definite or negatively definite with non-negative diagonal elements of A.

Thank you.

Colby Messinger answered 1 year ago

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