Robert J. Guyan proposed a method for reducing the stiffness and mass matrices in structural analysis. This technique is similar to the reduction of the stiffness matrix in statical structural analysis, where coordinates with no applied forces are eliminated. The structural equations are rearranged into a partitioned form, and the forces in the second partition are set to zero. This leads to a reduced stiffness matrix, $ K_1 = A - BC^{-1}B' $, which represents the stiffness of the structure after coordinate elimination. The method also applies to the mass matrix. By applying the same transformation, the reduced mass matrix $ M_1 $ is derived as $ M_1 = T'KT $, where $ T $ is the transformation matrix. The reduced mass matrix involves combinations of stiffness and mass elements, resulting in a slightly altered eigenvalue-eigenvector problem. However, the reduced stiffness matrix retains all structural complexity, as all elements of the original stiffness matrix contribute. The reduction technique preserves the essential characteristics of the original system but introduces some approximation in the mass matrix. Comparative results for beam vibrations are reported in the literature, showing the effectiveness of this method in simplifying large-scale structural analysis problems. The method is a fundamental contribution to the field of structural dynamics and has been widely used in engineering practice.Robert J. Guyan proposed a method for reducing the stiffness and mass matrices in structural analysis. This technique is similar to the reduction of the stiffness matrix in statical structural analysis, where coordinates with no applied forces are eliminated. The structural equations are rearranged into a partitioned form, and the forces in the second partition are set to zero. This leads to a reduced stiffness matrix, $ K_1 = A - BC^{-1}B' $, which represents the stiffness of the structure after coordinate elimination. The method also applies to the mass matrix. By applying the same transformation, the reduced mass matrix $ M_1 $ is derived as $ M_1 = T'KT $, where $ T $ is the transformation matrix. The reduced mass matrix involves combinations of stiffness and mass elements, resulting in a slightly altered eigenvalue-eigenvector problem. However, the reduced stiffness matrix retains all structural complexity, as all elements of the original stiffness matrix contribute. The reduction technique preserves the essential characteristics of the original system but introduces some approximation in the mass matrix. Comparative results for beam vibrations are reported in the literature, showing the effectiveness of this method in simplifying large-scale structural analysis problems. The method is a fundamental contribution to the field of structural dynamics and has been widely used in engineering practice.