What are the nodal incidence matrices?

What are the nodal incidence matrices?. Nodal incidence matrices (NIM) are used for electrical network modeling. Any network consisting of larger number of branches or edges and nodes can be modeled through them. The purpose of modeling is to study the different characteristics of a network. For example the current in a particular branch or voltages are studied through them. This matrix transformation makes quite easy how to solve a network. Generally Gauss Elimination method: a computer based algorithm is used for solving such systems.

Rules for generating the nodal incidence matrices

The following rules are used for generating NIM.

Following these rules we can translate any network into matrix form.

How to convert a network into (NIM) ?

The rules for converting are as follows:

1-on vertical side we write down the number of nodes. As it can be seen there are four nodes in the following network. So there are four rows in the matrix.

2. On horizontal side we have 5 columns as there are five branches in the network.

3. if a particular branch enters a node then corresponding to that node and branch, the matrix entry will be marked as -1.

4-If a branch leaves a node, then there will be marked as 1

5-if a branch does not enter or leave a node, then the matrix entry will be marked as zero.

Example of Nodal Incidence Matrix.

“1example of nodal incidence matrices

Also watch here

https://www.youtube.com/watch?v=HkyGFEJkNWw&t=88s

 

Also read here

https://eevibes.com/mathematics/linear-algebra/how-to-calculate-eigen-values-and-eigen-vectors/

How to calculate eigen values and eigen vectors of a matrix?