Incidence Matrix

Find the incidence matrix of a system of five equations in five variables.

Create the following symbolic vector eqs containing five symbolic differential equations.

syms y1(t) y2(t) y3(t) y4(t) y5(t) c1 c3
eqs = [diff(y1(t),t) == y2(t),...
       diff(y2(t),t) == c1*y1(t) + c3*y3(t),...
       diff(y3(t),t) == y2(t) + y4(t),...
       diff(y4(t),t) == y3(t) + y5(t),...
       diff(y5(t),t) == y4(t)];

Create the vector of variables. Here, c1 and c3 are symbolic parameters (not variables) of the system.

vars = [y1(t), y2(t), y3(t), y4(t), y5(t)];

Find the incidence matrix A for the equations eqs and with respect to the variables vars.

A = incidenceMatrix(eqs, vars)

A =
     1     1     0     0     0
     1     1     1     0     0
     0     1     1     1     0
     0     0     1     1     1
     0     0     0     1     1