4 articles
Definite matrix
A definite matrix is a Hermitian (in the real case, symmetric) matrix whose quadratic form takes values of only one sign, classified as positive, negative, semidefinite, or indefinite.
Polar decomposition
The polar decomposition, or polar factorization, is a matrix factorization A = UH into a unitary or orthonormal-column factor U and a Hermitian positive semidefinite factor H.
Positive definite matrix
A positive definite matrix is a Hermitian or real symmetric matrix for which the quadratic form is positive for every nonzero vector, equivalently all its eigenvalues are positive.
Sylvester's criterion
Sylvester's criterion is a test in linear algebra that determines whether a symmetric or Hermitian matrix is positive definite by checking that all its leading principal minors are positive.