Assertion: matrix's eigenvalue | /r/HasProperty | positive
Facets:
value: both
type: DEGREE
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: If it is positive, then the eigenvalues are both positive, or both negative.
text: A Positive Definite Matrix must have positive eigenvalues.
text: A Hermitian matrix is positive definite if all its eigenvalues are positive.
text: Every real eigenvalue of A is positive.
text: If it is positive, then the eigenvalues are both positive, or both negative.
text: A positive definite matrix is a symmetric matrix where every eigenvalue is positive.
text: A symmetric matrix is positive-definite if and only if all its eigenvalues are positive, that is, the matrix is positive-semidefinite and it is invertible.
text: A symmetric matrix is positive-definite if and only if all its eigenvalues are positive.