- #1
Leo321
- 38
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Let A be a real nxn matrix.
What are the requirements of A for A+AT to be positive definite?
Is there a condition on eigenvalues of A, so that A+AT is positive definite?
Also I am not sure about the definition of a positive definite matrix. In some places it is written that the matrix must be symmetric, while in others it is defined for non-symmetric matrices. In many places I see theorems, which require a matrix to be positive definite and it is not clear to me if I can use it for non-symmetric matrices or not.
What are the requirements of A for A+AT to be positive definite?
Is there a condition on eigenvalues of A, so that A+AT is positive definite?
Also I am not sure about the definition of a positive definite matrix. In some places it is written that the matrix must be symmetric, while in others it is defined for non-symmetric matrices. In many places I see theorems, which require a matrix to be positive definite and it is not clear to me if I can use it for non-symmetric matrices or not.
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