Linear Algebra Done Right, fourth edition

Sheldon Axler

errata

All typos in the print version of the fourth edition of Linear Algebra Done Right that I know about are listed below. These typos have been corrected in the current pdf version dated 23 April 2025 (freely available here). The pdf version of the book available from Springer and on several other websites is older and does not include corrections to the typos below. Similarly, the Kindle version of the book does not include these corrections.

• page xii, second line of third paragraph: “infomal” should be “informal”. (corrected 20 December 2023)

• page 35, line 3 of Step 1: “w_m” should be “w_n”. (corrected 16 January 2024)

• page 85, last line of statement of 3.68: “V ” should be “W ” and “W ” should be “V ”. (corrected 29 December 2023)

• page 110, line 4: “is the 0 vector in V ” should be “equals 0 ∈ F”. (corrected 4 January 2024)

• page 124, line 12 from bottom: “W” should be “We”. (corrected 20 December 2023)

• page 144, second line of second paragraph in proof of 5.22: “all complex vector spaces” should be “all vector spaces”. (corrected 20 December 2023)

• page 151, Exercise 4: Assume that p is a nonconstant polynomial. (corrected 29 November 2024)

• page 152, Exercise 13: Assume that V is finite-dimensional. (corrected 16 November 2024)

• page 157, line 6: “v₁” should be “v₂”. (corrected 20 December 2023)

• page 157, line 9: “v₁” should be “v₃”. (corrected 20 December 2023)

• page 166, first line: “nonzero” should be inserted after “a”. (corrected 25 March 2024)

• page 169, third sentence in last paragraph: “Every vector” should be “Every nonzero vector”. (corrected 11 February 2025)

• page 175, last paragraph, including the italicized note: “pairs” should be “ordered pairs”, four times total. (corrected 18 October 2024)

• page 179, line 8 above Exercises: “5B” should be “5C”. (corrected 12 January 2024)

• page 216, second line above 6.58: “be” should be “by”. (corrected 1 October 2024)

• page 229, paragraph above 7.4: Interchange “V ” and “W ”. (corrected 23 January 2024)

• page 234, second to last line of proof of 7.13: “U ” should be “V ”. (corrected 23 January 2024)

• page 244, third line of proof of 7.27: “see 6.69” should be “see 4.13”. (corrected 9 January 2024)

• page 259, third line from end of proof of 7.49: “Fⁿ ” should be “F^m ”. (corrected 25 January 2024)

• page 267, line 14 from bottom: “left” should be “right”. (corrected 27 January 2024)

• page 272, line 11: “7.64(c)” should be “7.64(d)”. (corrected 19 March 2024)

• page 276, second and third lines from bottom: “orthogonal” should be “orthonormal”. (corrected 20 February 2024)

• page 292, line 4 above 7.110: The last “Ω₁” on this line should be “Ω₂”. (corrected 13 March 2024)

• page 320, second line of proof of 8.41: “8.22(c)” should be “8.22(b)”. (corrected 5 February 2024)

• page 321, line 3 (not counting the title line) of Example 8.43: “contraast” should be “contrast”. (corrected 25 January 2024)

• page 336, third line from bottom of proof of 9.7: An open parenthesis should be inserted before “f₁”. (corrected 25 March 2024)

• page 339, lines 6, 7, and 8 of proof of 9.13: “C ^-1TC ” should be “C ^-1BC ”. (corrected 16 January 2024)

• page 339, line 8 of proof of 9.13: “C ^tTC ” should be “C ^tBC ”. (corrected 16 January 2024)

• page 341, lines 2 and 4 from bottom: The sum from j=1 to k should be a sum from j=1 to n. (corrected 25 September 2024)

• page 360, parts (d) and (e) of 9.57: “to added” should be “is added”. (corrected 13 June 2024)

• page 361: Each of the first three appearances of “9.48” in the paragraph after the proof should be “9.57”. (corrected 19 February 2024)

• page 366, matrix near bottom of page: The subscript “2” in row 3, column 2 should be “3”, the subscript “2” in row n, column 2 should be “n”, and both subscripts “3” in row n, column 3 should be “n”. (corrected 19 February 2024)

• page 367, last line: “det V ” should be “det T ” and “V has” should be “T has”. (corrected 27 February 2024)

• page 369, comment after Exercise 21: “denotes set” should be “denotes the set”. (corrected 2 January 2025)

• page 373, line 4 from bottom, and page 376, one line below 9.81: “V × W ” should be “V ⊗ W ”. (corrected 11 March 2024)

• page 377, fourth line of proof of 9.83: Interchange “N ” and “M ” (three times). (corrected 11 March 2024)

• page 385, top of first column: The index entry for “Bessel's inequality” should be moved to follow the index entry for “Bernstein polynomials”. (corrected 1 January 2024)

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