On the Relation Between Condensed Matrix and Its Determinant

EasyChair Preprint 6589

Abstract

In the present work, relations are established for the calculation of determinants, using an algebraic technique of Seismic Engineering called "Static Condensation", which is a process of reduction by blocks, of the order n of the stiffness matrix K_n. Through an inverse approach, the condensation process is applied (n-1) times until obtaining the maximum possible condensation K^c (1x1 matrix), reaching a relation between the determinant of K_n, the determinant of the K_(n-1) submatrix, and K^c. Finally, a relation is established between the determinant of K_n, the determinant of one of its simple intermediate condensates K_p^* and the simple main sub-condensates k_i^*.

Keyphrases: Ingeniería Sísmica, Matriz Condensada, Reducción Estática de Guyan, determinante, Álgebra Lineal

@booklet{EasyChair:6589,
  author    = {Victor Leighton Inostroza},
  title     = {On the Relation Between Condensed Matrix and Its Determinant},
  howpublished = {EasyChair Preprint 6589},
  year      = {EasyChair, 2021}}