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From the Sylvester criterion [31] it follows that we can verify that the matrix is positive definite by calculating its leading principal minors, that is, by verifying the positivity of (3n+1) determinants.
so the matrix is positive semi-definite.
Assume that matrix is positive definite.
Hence, the given matrix is positive semidefinite.
(a)For every and, the matrix is positive semidefinite.
Since the matrix is positive definite, we have (3.6).
From this we have that the matrix is positive semidefinite.
Because all eigenvalues are positive, matrix is positive definite.
Because all the eigenvalues are positive, matrix is positive definite.
Moreover, the realizing matrix is positive if (3.2), (3.4), (3.5), and (3.6) are all strict inequalities.
This means that the matrix is positive semidefinite, that is, (2.9) is valid.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com