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 were corrected in the fourth edition.

• 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(v_k)” should be “M(Tv_k)”.

• 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 “u_n” should be “v_n”.

• 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, ... , v_j)” should be “restricted to span(v₁, ... , v_j)”.

• 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 “E(λ_j, T)”.

• page 161, Exercise 15: “F³” should be “C³”.

• page 166, line before Example 6.4: “w” should be “u”.

• page 168, line 1: “(a)” should be “(b)”.

• page 175, Exercise 5: Assume that V is finite-dimensional.

• page 177, Exercise 17: The right side of the displayed equation should be “max{|x|, |y|}”.

• page 177, Exercise 18: The right side of the displayed equation should be “(|x|^p + |y|^p)^1/p ”.

• page 183, line 4 of Proof: “1 < j < m” should be “1 < j ≤ m”.

• 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 v ∈ V” 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: “λ_m” should be “λ_j”.

• page 277, 11 lines from bottom: “Im_n” should be “Im λ_n”.

• 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 “λ_nr” should be “λ_nr_n”.

• page 325, line 7 of the proof of 10.52: “Ω” should be “B”.

• page 326, first line of proof of 10.54: “V ” should be “Rⁿ”

• page 329, line 11: “y = f(x)” should be “y = σ(x)”.

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