Linear Algebra, Third Edition

by Michael O'Nan and Herbert Enderton

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The book is out of print by Harcourt. When we used the book here at UCLA, spiral-bound copies were made (with permission) by Academic Publishing Service, and sold at the UCLA bookstore for under $30. It may still be available there by special order.

History: The first and second editions were by Michael O'Nan. When the time came for a third edition, he did not want to prepare it. The publisher then approached the second author, who had used the second edition and had definite views on how it should be changed. He then made the revisions for the third edition. The two authors have never met.

Summaries:

• Here is a summary of the methods in Chapter 4 in pdf format.
• Here is a summary of the methods in Chapter 5 in pdf format.
• Here is a summary of the methods in Chapter 6 in pdf format.
• Here is a summary of the methods in Chapter 7, Sections 1-2, in pdf format.

Upgrades:

• Page 206. Here is an improved version of the second half of page 206 in pdf format.
• Page 310. The parenthetical observation on this page, that matrices are similar if and only if they represent the same linear operator relative to possibly different bases, should be presented as a theorem.
• Page 358. The proof of the Cauchy-Schwarz inequality is simpler if we apply the Pythagorean formula: |p|^2 + |e|^2 = |u|^2.
• Page 405, Section 7.3. Here is an improved version of pages 405-410, on symmetric operators and the spectral theorem in pdf format.

Errata: First of all, the correct spelling of kernel is K-E-R-N-E-L. No other spelling is acceptable. (I can't understand how this error got past me.)

Other more local corrections:

• Page 8, line 3. The second equation should be 6x + 9y + 3z = 9 (that is, one of the z's should be a y).
• Page 12, Example 3. In the last equation of the given system, the coefficient of x_1 should be 3 (not 1).
• Page 137, Example 4. Here (and elsewhere), "functions" are to be understood as "real-valued functions." [More generally, functions taking values in a field F give a vector space over F; the book does not go into this.]
• Page 157, Exercise 15: Assume that H is nonempty.
• Page 159, line 9 from below. Here "passes the origin" should be "contains the origin."
• Page 162, second displayed equation, bottom row. There is a missing subscript (of 1) on the first alpha.
• Page 179, Exercise 14. The last occurrence of d_1 should be lightface italic.
• Page 190, Exercise 20. Here "sigma_2" should be "sigma_z."
• Page 249, Exercise 13, part (b). There is a missing right parenthesis.
• Page 299, Exercise 28. In the displayed equation for the new addition operation, on right side replace x + y + t by x + y - t.
• Page 366, line 2 from below. "First, v_1 = x" should instead read "First, v_1 = 1."
• Page 409, Example 3. It should be understood that U is to be orthogonal.
• Page 447, Exercise 20. The last equation on page 447 is not the one that yields the conclusion on the next page. Instead of showing the three given columns to be independent, one must first show that the three rows are independent.
• Page 454, Exercise 17(a) (for Section 7.2). The matrix given is the diagonal matrix D, not the matrix B specified by the problem.

Readers are encouraged to send further corrections to the second author: