Matrices that are similar to triangular matrices are called triangularisable. Some estimators are highly sensitive to outliers, notably estimation of covariance matrices. It consists of all orthogonal matrices of determinant . These questions led extending algebra to non-numerical objects, such as permutations, vectors, matrices, and polynomials. They are equivalent to rotation matrices and rotation vectors. The set of positive semidefinite symmetric matrices is convex. There are a total of nine possibilities using scalars, vectors, and matrices. Subsequent sections describe methods suitable for numerical evaluation on large matrices. Below are a few examples of small orthogonal matrices and possible interpretations. Denote by formula 13 the space of all formula 7 real symmetric matrices. H denote the set of positive definite Hermitian matrices. These articles give the explicit formulae for the composite transformation matrices, including expressions for . Writing formula 65 with formula 33 and formula 67 real symmetric matrices, formula 68. This procedure for finding the inverse works for square matrices of any size. Special algorithms have been developed for factorizing large sparse matrices.