## Textbook

Using Matrices and Linear Transformations by Charles Cullen (Dover, ISBN 0-486-66328-0).

## Worked Solutions/Elaborations

I'm experimenting with using Mathematica as an aid for problem solving and deeper insight, and as mathematical typesetting. It's an excellent tool for checking manually calculated answers to problems; even when a solution is provided in the book, it will help me find mistakes in intermediate steps. As a typesetting tool it comes up somewhat short: while it does mostly get the job done, there is a lot of typing overhead involved. Also, the results don't look anywhere near as good as XeTeX.
1. Chapter 1

Comments on the book. Elaborations on theorem proofs, et cetera, are in the worked solutions.

## Notation

This is notation used by the author that is archaic or otherwise not currently standard; also, notation of my own that I believe to be more consistent or logical than the accepted standard that I've used in the worked solutions.

 Author Standard Mine Meaning ∋ : “such that” ${ℱ}_{𝘮⨯𝘯}$ ${𝔽}^{𝘮⨯𝘯}$ field of m-by-n matrices $\stackrel{̅}{𝘻}$ $\stackrel{̅}{𝘻}$ or ${𝘻}^{*}$ ${𝘻}^{*}$ complex conjugate ${\sum }_{𝘪}$ ${+}_{𝘪}$ summation over i ${ent}_{𝘪𝘫}$ $\left[𝗔\right]$𝘪𝘫 the element in the ith row and jth column of 𝗔 $𝗑$, $𝖷$, $𝖷$ $𝗑$, $𝘅/\stackrel{̅}{𝗑}$, $𝗫/𝖷$ $𝗑$, $𝘅/\stackrel{̅}{𝗑}$, $𝗫/\stackrel{̿}{𝖷}$ scalar, vector, matrix

I welcome any comments or corrections to the solutions.