equations become where equ6 the foregoing steps have converted the system equations to modal form using eigenvalues and eigenvectors the rows of cc indicate which instruments are responding to which modes a zero or a very small number relative to the other elements in the same row in the i th row j th column indicates that the i th instrument is not responding to the j th mode to establish which instruments are related a normalization procedure may be carried out each element in a row is divided by the magnitude of the element in that row having the maximum magnitude then to facilitate examination of the resulting matrix all elements below a certain threshold value are set equal to zero when this procedure is applied to the matrix cc using a threshold value 0 01 the matrix ccf shown below is obtained equ7 note that each row of the ccf matrix corresponds to a particular instrument rows 1 through 8 correspond to instruments y 1 through y 8 if a particular instrument reading is to be estimated by another set of instruments then at least one member of the other set should have a nonzero entry in every column that the instrument to be estimated has a nonzero entry for example examining ccf it is seen that row 1 corresponding to instrument y 1 has a nonzero entry only in columns.