Assertion: matrix's root | /r/HasProperty | positive-definite square
Facets:
Source sentences:
text: This also leads to a proof of the above observation, that a positive-definite matrix has precisely one positive-definite square root: a positive definite matrix has only positive eigenvalues, and each of these eigenvalues has only one positive square root; and since the eigenvalues of the square root matrix are the diagonal elements of D½, for the square root matrix to be itself positive definite necessitates the use of only the unique positive square roots of the original eigenvalues.
text: However, a positive-semidefinite matrix has precisely one positive-semidefinite square root, which can be called its principal square root.