Analysis of discrete systems The essence of a lumped-parameter mathematical model is that the state of the system can be described directly with adequate precision by the magnitudes of a finite (and usually small) number of state variables. The solution requires the following steps: System idealization: the actual system is idealized as an assemblage of elements Element equilibrium: the equilibrium requirements of each element are established in terms of state variables Element assemblage: the element interconnection requirements are invoked to …

Special Matrix symmetric matrix identity matrix / unite matrix symmetric banded matrix the following matrix is a symmetric banded matrix of order 5 and the half-bandwidth is 2. \[{\rm{A}} = \left[ {\begin{array}{*{20}{c}} 3&2&1&0&0\\ 2&3&4&1&0\\ 1&4&5&6&1\\ 0&1&6&7&4\\ 0&0&1&4&3 \end{array}} \right]\] diagonal matrix: nonzero elements only on the diagonal of the matrix upper half of the matrix inverse matrix, the inverse of a matrix partitioning of matrix the trace and determinant of a matrix: only defined if the matrix is square tr(A) …