Matrix Visualizer

This shows the transformation of a matrix with row 1 being 1 and 2, and row 2 being 3 and 4. Visualization and its characteristics are shown

Inspiration: I was inspired by this because I wanted to fully understand the idea regarding linear transformations in linear algebra and also for others to understand how it works as well.

What it does: This program shows what happens to the standard basis vectors e1 and e2 after a matrix that is either preset and you just press a button to see the transformation, or the user can enter their own 2x2 matrix to see how it transforms the two vectors.

How we built it: I used IntelliJ, and here I was using Java Swing in order to make everything visual. There were two files: GridPanel and MatrixWindow. GridPanel mostly controlled the graph (grid/vectors), and MatrixWindow the buttons, labels, and user input.

Challenges I ran into: First, I had to fully understand the transformations in order to figure out if I was making any mistakes with my code. Second, I struggled drawing the grid without gaps due to there being a low grid space. Third, I found it difficult to distinguish between standard basis vectors and transformed vectors, so I needed to utilize different colors to my advantage. Lastly, I had to account for many different preset transformations.

Accomplishments that I am proud of: This was one of the few Java Swing programs I have made. In this program, I was able to get the user to enter a 2x2 matrix, dealing with the input, and visualize the effects for them, I made a dynamic coordinate grid visualization, I had many preset transformations, and I got a much better understanding of linear algebra as a whole.

What I learned: I learned about how Java Swing can be so useful and how programming can be useful for people to understand difficult math such as linear algebra.