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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.



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”
𝘮𝘯 𝔽𝘮𝘯 field of m-by-n matrices
𝘻̅ 𝘻̅ or 𝘻* 𝘻* complex conjugate
𝘪 +𝘪 summation over i
ent𝘪𝘫 𝗔𝘪𝘫 the element in the ith row and jth column of 𝗔
𝗑 , 𝖷 , 𝖷 𝗑 , 𝘅/𝗑̅ , 𝗫/𝖷 𝗑 , 𝘅/𝗑̅ , 𝗫/𝖷̿ scalar, vector, matrix

I welcome any comments or corrections to the solutions.

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