a symmetric matrix is a square matrix, A, that is equal to its transpose and An n × n real symmetric matrix M is positive definite if zTMz > 0 for all non-zero vectors z with real entries (i.e. z ∈ Rn), where zT denotes the transpose of z.
a symmetric matrix is a square matrix, A, that is equal to its transpose and An n × n real symmetric matrix M is positive definite if zTMz > 0 for all non-zero vectors z with real entries (i.e. z ∈ Rn), where zT denotes the transpose of z.
There is a theorem telling that (here, ) is positive definite if, and only if, for the determinant of is positive.
If you know this, then it is easy. The determinants of are positive, they do not depend on , and the determinant of is found to be , hence it is positive iff . So is positive definite iff .