First open the application by running the gui.py app. A window should pop up which shows a textbox, a Generate button and an Exit button. To find the number of invariant subspaces and the jordan form of an n x n matrix (where 1 <= n <= 20 since anything more would take a long time for the application to compute). Another window will pop-up with blank textboxes and from there, you can fill in the numbers for your matrix. After doing that, you would click the compute button and another window will pop up and tell you how many invariant subspaces there are and the jordan form for the matrix that was inputted.
It might take longer for bigger matrices (anything bigger than 4x4) since python is slow :(