# incidenceMatrix

Find incidence matrix of system of equations

## Syntax

``A = incidenceMatrix(eqs,vars)``

## Description

example

````A = incidenceMatrix(eqs,vars)` for `m` equations `eqs` and `n` variables `vars` returns an `m`-by-`n` matrix `A`. Here, `A(i,j) = 1` if `eqs(i)` contains `vars(j)` or any derivative of `vars(j)`. All other elements of `A` are `0`s.```

## Examples

### 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```

## Input Arguments

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Equations, specified as a vector of symbolic equations or expressions.

Variables, specified as a vector of symbolic variables, symbolic functions, or function calls, such as `x(t)`.

## Output Arguments

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Incidence matrix, returned as a matrix of double-precision values.

## Version History

Introduced in R2014b