Home:Academic:Mathematics:Matrices and Linear Transformations

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.

Chapter 1

Comments

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

Observations

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
$\overset{̅}{𝘻}$	$\overset{̅}{𝘻}$ or $𝘻^{*}$	$𝘻^{*}$	complex conjugate
$\sum_{𝘪}$		$+_{𝘪}$	summation over i
${ent}_{𝘪𝘫}$		$[𝗔]$ _𝘪𝘫	the element in the ith row and jth column of 𝗔
$𝗑$ , $𝖷$ , $𝖷$	$𝗑$ , $𝘅 / \overset{̅}{𝗑}$ , $𝗫 / 𝖷$	$𝗑$ , $𝘅 / \overset{̅}{𝗑}$ , $𝗫 / \overset{̿}{𝖷}$	scalar, vector, matrix

I welcome any comments or corrections to the solutions.