SPDMatrizen
SPDMatrizen, in English symmetric positive definite matrices, are real square matrices that are symmetric (A^T = A) and satisfy x^T A x > 0 for all nonzero vectors x. This condition is equivalent to A having strictly positive eigenvalues, or to the existence of a Cholesky factorization A = L L^T with a lower triangular L and positive diagonal entries. SPD matrices can also be written as A = Q Λ Q^T with Q orthogonal and Λ diagonal with positive entries, reflecting their positive-definite nature.
SPD matrices form a convex cone inside the space of symmetric matrices: if A and B are
Applications of SPD matrices are common in optimization, statistics, and numerical linear algebra. They define valid