Assertion: orthogonal matrix | /r/HasProperty | positive-definite
Facets:
Source sentences:
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: If the quadratic form f yields only non-negative values (positive or zero), the symmetric matrix is called positive-semidefinite (or if only non-positive values, then negative-semidefinite); hence the matrix is indefinite precisely when it is neither positive-semidefinite nor negative-semidefinite.
text: A symmetric matrix is positive-definite if and only if all its eigenvalues are positive.
text: If the quadratic form takes only non-negative (respectively only non-positive) values, the symmetric matrix is called positive-semidefinite (respectively negative-semidefinite); hence the matrix is indefinite precisely when it is neither positive-semidefinite nor negative-semidefinite.