Essence of Linear Algebra: Revised Linear Transformations Lesson

[kurtbruns]

This pull request publishes these changes for the "linear transformations" lesson:

• Publishes vectorized images and animations consistent with the series
• Adds multiple new questions to the article
• Changes perspective to be plural
• Adds attribution for James

Notes:

• Structurally the biggest change was moving the "formal properties" into their own section. I think this best preserves the original intent that the lesson be visually motivated. Note: these formal properties are explicitly referenced in the "dot products" lesson. Possibly they could live in a stand-alone lesson. I didn't realize this part was scripted as it's just a frame at the very end frame of the video, so I modified what River had already written. See the very end of the original script for reference.
• @3b1b What are your thoughts on keeping the original input vector in the visuals during the "transformations are functions" section?

[3b1b]

Looking good, there are just a few small things I noticed.

- In the image matrices/MatrixNotation2x2.svg, the opening quotation marks are backwards. In LaTeX, you'd want to use "``"

- I found the diagram matrices/MatrixNotation2x2InputOutput.svg and matrices/MatrixNotation2x2InputOutputGeneral.svg a little bit confusing. They sort of make it look like the input vector gets turned into the matrix, which gets turned into the output vector. Instead, I might draw it where you have the input vector on the top, a big downward arrow to the output vector on the bottom, and display the matrix next to that arrow. Hopefully, this would better convey the idea that the matrix is the transformation.

Other than that, the graphics are great as usual, and the questions are all well-chosen. To your question on keeping the input vector in the graphics of "transformations are functions", I like the way you have it here.