Operations on symmetric matrices

LDLT decomposition
Factorization of a symmetric indefinite matrix

Determinant of a symmetric positive definite matrix
Cholesky decomposition is used

Determinant of a symmetric indefinite matrix
LDLT decomposition is used

Inverse of a symmetric indefinite matrix
LDLT decomposition is used

Condition number estimate of a symmetric indefinite matrix
Cholesky decomposition is used

Reduction of a symmetric matrix to tridiagonal form
Reduction of a symmetric matrix to tridiagonal form by the orthogonal similarity transformation.