# Linear Algebra Done Right

## Third Edition Errata

I tried hard to make Linear Algebra Done Right error-free, but spotting mistakes in one's own writing can be difficult in a book-length work. All errors in the third edition that I know about are listed below. These errors will be corrected in the next printing. If you notice additional errors in the book or have suggestions for improvements, please let me know (`linear@axler.net`).

• page xiii, line 8: “that that” should be “that”.
• page 3, Example 1.4: There is no need to mention λ.
• page 6, third line above 1.10: The word following “replace” should be “the”.
• page 59, first line in second bullet point: “L(C3, F)” should be “L(C3, C)”.
• page 72, line 6: “T” should be “D”.
• page 85, lines 2, 4, 7, and 9: “M(vk)” should be “M(Tvk)”.
• page 98, third line of proof of part (b): “0” should be “{0}”.
• page 114, Exercise 18: Assume that U is a nonempty subset of V.
• page 115, last line: The second “un” should be “vn”.
• page 123, ten lines from bottom: “its proof” should be “in its proof”.
• page 130, Exercise 11, part (b): Delete “dim”.
• page 138, first line of Solution (b): “V” should be “F2”.
• page 151, sixteen lines from bottom: “restricted to dim span(v1, ... , vj)” should be “restricted to span(v1, ... , vj)”.
• page 153, Exercise 8: “-1” should be “-I”.
• page 153, Exercise 11: “polynomial” should be “nonconstant polynomial”.
• page 156, third line of proof of 5.38: “E(λ, T)” should be “Ej, T)”.
• page 161, Exercise 15: “F3” should be “C3”.
• page 166, line before Example 6.4: “w” should be “u”.
• page 175, Exercise 5: Assume that V is finite-dimensional.
• page 177, Exercise 17: This is a better exercise if the right side of the displayed equation is “max{|x|, |y|}”.
• page 177, Exercise 18: This is a better exercise if the right side of the displayed equation is “(|x|p + |y|p)1/p ”.
• page 183, line 4 of Proof: “1 < j < m” should be “1 < jm”.
• page 193, first line after 6.45: “line in R3” should be “line in R3 containing the origin”.
• page 193, second line after 6.45: “plane in R3” should be “plane in R3 containing the origin”.
• page 229, line 9: “basis” should be “orthonormal basis”.
• page 232, Exercise 11: “on” should be “in”.
• page 239, Exercise 6: The first “P(R2)” should be “L(P2(R))” and the second “P(R2)” should be “P2(R)”.
• page 240, Exercise 17, part (d): The phrase “for every vV” is redundant and should be deleted.
• page 247, displayed equation three lines above 8.15: The second “w” should be “v1”.
• page 252, line before 8.20: “is” should be “are”.
• page 268, Exercise 7: “T” should be “P”.
• page 273, second line from bottom: “λm” should be “λj”.
• page 277, 11 lines from bottom: “Imn” should be “Im λn”.
• page 284, fourth line of proof of 9.23: “8.36(a)” should be “8.36(b)”.
• page 325, line 6 of the proof of 10.52: “λ1r” should be “λ1r1” and “λnr” should be “λnrn”.
• page 325, line 7 of the proof of 10.52: “Ω” should be “B”.
• page 329, line 11: “y = f(x)” should be “y = σ(x)”.