Inclusion Monotonic Property of Courant–Fischer Minimax Characterization on Interval Eigenproblems for Symmetric Interval Matrices

[[abstract]]The classical Courant–Fischer minimax theorem for symmetric matrix is extended to the interval symmetric matrix. Inclusion monotonic prop- erty for interval version of Courant–Fischer theorem is discussed in this article and proved. By introducing the center–radius representation of the symmetric interval matrix and sign matrices with respect to the eigenvec- tors of the center matrix, the interval Courant–Fischer minimax equation is split into two ordinary minimax equations corresponding to the lower bound and upper bound eigenvalues. The two minimax equations are thus equivalent to two ordinary eigenvalue problems. The assumption that the signs of the elements of the eigenvectors are not changed for ma- trices ranging over the intervals is applied and is crucial on determining the sign matrices. A simple example demonstrate the algorithm presented in this article