## 2021: First EditionTea Time Linear Algebra Explorations in Mathematics

#### Changelog (last updated 2022 Jun 16)

These changes do not appear in the print version or the main download (the pink "Download PDF" link at the top of this page).
##### 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

#### 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!