Meaning of Incidence matrix?

Specific Domains Modelling & Simulations
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1

I defined a nonlinear model and linearized it. I get the following result:

julia> simplified_sys
Model sys with 3 equations
States (3):
  ω(t) [defaults to 1.04286]
  Uest(t) [defaults to 9.0]
  Pgc(t) [defaults to 2.46048e6]
Parameters (9):
  J [defaults to 4.047e7]
  Ku [defaults to 2.25e-7]
  λnom [defaults to 7.3]
⋮
Incidence matrix:3×6 SparseArrays.SparseMatrixCSC{Num, Int64} with 12 stored entries:
 ×  ⋅  ×  ×  ⋅  ⋅
 ×  ×  ×  ⋅  ×  ⋅
 ×  ×  ×  ×  ⋅  ×

What is the meaning and the relevance of the Incidence matrix?

2

If any of the actual developers of this code choose to respond, they probably know better. But if-I-understand-correctly, the sparse incidence matrix shows how the new simplified state variables depend on the original state variables. So in the example above ω(t) would depend on 3 variables of the pre-simplified formulation. And the same applies to the other new variables.

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3

The incidence matrix a structural representation of which variables occur in which equations. The rows are the equations of the system, the columns are the variables.

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4

Thank you!