Technical Terms Positive Definite Matrix: A symmetric (or Hermitian) matrix with all eigenvalues positive, ensuring properties such as stability and invertibility.

We succeed to introduce a general structure of symmetric matrices which unifies the theroy of graphical model and the theory of homogeneous cones. Based on this discovery, we will evaluate, improve ...

In this paper we consider estimating the rank of an unknown symmetric matrix based on a symmetric, asymptotically normal estimator of the matrix. The related positive definite limit covariance matrix ...

Combination of real and imaginary parts (CRI) works well for solving complex symmetric linear systems. This paper develops a generalization of CRI method to determine the solution of Sylvester matrix ...

We succeed to introduce a general structure of symmetric matrices which unifies the theroy of graphical model and the theory of homogeneous cones. Based on this discovery, we will evaluate, improve ...