On December 3, 2009, Thursday, 15.00, in room 407 of the University of Georgia, there was a seminar on the topic “Centrosymmetric matrices of one type in eigenvalue problems”. The seminar was presented by Dr Liana Karalashvili. There is considered general form of the third order matrices, which are at the same time symmetric, too and have such a property that sum of elements in each row is the same number. The characteristic equation of such matrices is constructed in a factorized form. All eigenvalues and eigenvectors are given in an explicit form. Besides, such type of matrices have the same eigenvectors. There is constructed a matrix of spectral decomposition (its columns represent orthonormal eigenvectors of the initial matrix) and its inverse, which reduce the initial matrix to the diagonal matrix. It gives a possibility to evaluate any degree of the given matrix.