Understanding Matrices and Matrix Multiplication

Matlab actually stands for matrix laboratory, and one of its principal features is its state-of-the-art ability to calculate computationally intensive matrix products and inverses! Here, you'll put programming aside for a minute to establish a framework to understand what matrices are, and what their multiplication represents, so that you can understand how, and recognize when, these aspects come up throughout an enormous diversity of programming applications.

Task

If you had trouble with any of the concepts in the video, your task is to:

1. Spend some time reviewing the diagram + examples provided, and/or researching a particular topic online;

2. Rewatch the video with the goals of getting a bit more familiar, and understanding the statement of the main results we'll be using in applications in the remaining chapters:

   • Once bases have been chosen: every linear transformation is represented by a unique matrix, and every matrix represents a unique linear transformation;
   • Matrix multiplication outputs the unique matrix that describes the composition of the two transformations represented by the matrix in the product.

A deeper understanding of the content will naturally allow you to open more doors in your programming applications.

Recursive programming, like while loops, has the potential to jump down rabbit holes if there’s a bug. If you find your program is taking too long, hit Ctrl+C or Command+C in the command window to stop it from running, and reanalyze your code.

You might have to ensure that any hidden system files appear at the top of the list in the directory returned by the dir function. This should be the case, but if it's not, you'll need to find a more creative means of eliminating them from recursive calls. Long program run times would be symptomatic of this problem.