#### Changelog `1^(st)` edition to `2^(nd)` (last updated 2022 Jul 14)

#### Introduced in the second edition

- Default typesize decreased from 12pt to 10pt
- Free, complete course management at MyOpenMath including randomly generated versions of most exercises now available. Course shell fully aligned to textbook available from the course browser. Request an instructor account to access.

##### Changes (do not appear in the `1^(st)` edition print version or previous version download)

##### Chapter 1

**P 10:**"matrix" changed to "block"**P 11:**lower case letters for entries capitalized in definition of matrix subtraction**P 20:**exercise 1, column matrix times row matrix examples removed**P 21:**exercise 8, added clarification that `mathbf(u)` and `mathbf(v)` have the same number of entries**P 22:**added exercises on computing dot product in SageMath**Section 1.4:**"length" changed to "magnitude" (also modified throughout the text)**P 25:**clarification of the calculation**P 29:**exercise 6d, `mathbf(u)` and `mathbf(v)` swapped**P 44:**added questions about existence of inverses; TODO move exercise 4**P 45:**hint added to exercise 7; exercise 10 moved to section 1.5**P 48:**demonstration of the unusualness of eigenvectors added

##### Chapter 2

**P 57:**shorthand provided in summary of elementary row operations**P 59:**clarification added to instructions of exercise 2**P 60:**exercises on elementary matrices added**P 69:**exercise 5, `a,b,c` specified as arbitrary real numbers**P 73:**paragraphs one and two adjusted**P 74:**crumpet 15, last sentence corrected**P 76:**synchronized the matrix and the code**P 78:**clarification of instructions for exercises 7 and 10

##### Chapter 3

**P 84:**added "and all scalars `r,s` to theorem 3**P 85:**theorem 4 part 3 inserted: `(rA)^-1=1/r A^-1`; justification for theorem 4 claim 6 now requested in exercises**P 86:**"rule" changed to "property"**P 87:**several "calculate this without calculating that" exercises added**P 90:**removed spurious "as well"**P 94:**exercises 12 and 13 reworded**P 101:**solution reference in exercise 4 fixed**P 102:**exercise 17 and the preamble to exercises 20-21 reworded**P 104:**parts (vi) and (vii) of theorem 6 swapped**P 109:**added explanation of the "trick"**P 120:**`ME` changed to `EM`**P 122:**"both" removed from crumpet**P 129:**parentheses added to `det(MB)` in exercise 3**P 130:**claim in exercise 6 slanted

##### Chapter 4

**P 139**list of vector spaces trimmed down by 2 that were never used (one because it was not a vector space!); instructions in exercise 2 clarified**P 142**instructions for exercises 21, 23, and 26 corrected**P 143**order of equalities reversed**P 144**preliminary discussion clarified**P 147**"proper" inserted in exercise 4; `t^2` inserted in exercise 7**P 152**definition of kernel generalized**P 154**ordered pair added to exercise 1c; "the" changed to "a" in exercise 11**P 155**`n` and `m` swapped in exercise 14; "linear" changed to "a linear transformation" in exercise 17**P 163**brown line clarified**P 164-167**collected all exercises involving rotation into a section at the end of the exercises**P 167**added an exercise on reflection about a line other than the axes**P 169**bolded "isomorphism" and "isomorphic"; inserted "corresponds" in penultimate paragraph**P 171**added an exercise on identifying one-to-one functions; added an exercise on identifying onto functions; rephrased exercises 1 and 2; added "linear?" to exercises 3 and 4; added a third exercise like 3 and 4**P 176**fixed refrence in footnote**P 177**changed `1/(2pi)` to `1/pi` in exercise 1f; simplified wording of exercises 2-13**P 179**eliminated exercise 15c

##### Chapter 5

**P 184**added a sentence to the explanation that row operation do not affect linear dependence relationships**P 185**renamed parameters in the parametric form**P 188-191**clarified the statements of 6 exercises**P 195**added four exercises on calculating a vector given a coordinate vector**P 195-197**removed a redundant exercise and clarified another**P 202-204**much of the discussion moved to a crumpet**P 206-207**several exercises clarified**P 217**exercise 4 modified, part b added to exercise 6

##### Chapter 6

**P 226-227**clarified exercises**P 232**reworded list item (iii) to use eigenspace dimension**P 232-233**clarified notation for the dominant eigenvalue and associated quantities by subscripting with `d` instead of `j`**P 234**replaced `M` by `mathbf(v)_6` in exercise 3 and reworded the instructions**P 235**minor revisions to exercises 6 and 8**P 236**rewrote exercise 14**P 243**clarified exercises 2,4,5**P 244**added exercise 13**P 250**corrected definition of orthogonal projection in lise of key concepts**P 252**replaced exercise 3h**P 253**minor revision to exercise 7

##### Chapter 7

**P 257**minor rewording**P 258**minor rewording; changed "theorem" to "corollary"**P 260**added explanation of linear variation of parameters**P 263**clarified crumpet 29 bullet point 1**P 264**clarifications to exercise 1**P 265-266**swapped method requested in exercises 3 and 4 and fixed solutions and answers**P 276**changed "sector" to "industry" in exercise 9 and clarified**P 277**changed numbers in exercise 11**P 281**removed special treatment of case `m=0`**P 285-287**corrected formula for Fourier coefficients**P 288**added two parts to exercise 7; added "the first" to exercises 8-10; replaced `V_([0,L])` notation in Answers**P 289**replaced `V_([0,L])` notation**P 290**simplified explanation of brownie experiment**P 292**clarified the role of Newton's law of cooling**P 294**vocabulary correction**P 295**added the term "long run behavior"**P 298**clarified analogy between geometric series and discrete dynamical systems**P 299**added some explanation of asymptotic periodicity**P 300**added several parts to exercise 1 and modified existing parts**P 301**fixed equations in exercises 10 and 11**P 302**clarified linearization**P 310**changed 50 to 60 in footnote**P 312**extended the hint in exercise 12

##### Answers and Solutions

**P 315-413**corrected, supplemented, and synchronized many answers and solutions

#### PDF with revisions

A PDF with these revisions and numerous bug fixes is available for download here. This version will always be the most up-to-date revision and will change regularly. You might consider this a preview of the next edition. Suggestions welcome at`brinl1@southernct.edu`!