Matrix Algebra: Theory, Computations and Applications in Statistics Second Edition

Errata and Clarifications

• Page 22, second bulleted statement:
  The statement should read "Let V be a vector space and let V1 be a subspace, Then there exist a basis B for V and a basis B1 for V1 such that B1 is a subset of B."
  (Thanks to Mirroslav Yotov and to Jenya Chelishchev (independently)!)
  
• Page 24, line 15:
  The definition of inner product does not include the statements about the 0 vector. The statements in property 1 about 0 follow from properties 2 and 3.
  (Thanks to Mirroslav Yotov!)
  
• Page 28, lines 20 and 21:
  should be "... we have shown ...and then we established ...".
  (Thanks to Mirroslav Yotov!)
  
• Page 30, line 15b:
  should be "r" should be "\tilde{r}".
  (Thanks to Timothy Fortune!)
  
• Page 41, equation (2.61):
  "k" should be "n".
  (Thanks to Shijia Jin!)
  
• Page 44, line 14:
  "v_1+v_2" should be "v_1-v_2".
  (Thanks to Shijia Jin!)
  
• Page 45, line 12:
  The inclusion of the duals is reversed;
  should be "C*(S_2) is a subset of C*(S_1), or C*_2 is a subset of C*_1".
  (Thanks to Cecilia Lucy!)
  
• Page 46, line 22:
  "a cone" should be "the cone".
  (Thanks to Shijia Jin!)
  
• Page 60, lines 5b and 2b:
  this only applies to diagonal matrices; line 2b should be
  "and if A is a square diagonal matrix,".
  (Thanks to Mirroslav Yotov!)
  
• Page 67, line 7 and 8:
  "The total number is 2q-2p+1", should be "The total number is 2q-2p-1".
  It is still odd, so the conclusion is the same.
  (Thanks to Zhilun Li!)
  
• Page 71, line 14:
  The factor "a_{m+1}j_n", should be "a_{m+1}j_{m+1}".
  (Thanks to Shijia Jin!)
  
• Page 87, lines 8b and 7b:
  The factor denoted "A_{(ij)}", should be the minor "A_{-(p)(j)}".
  (Thanks to Shijia Jin!)
  
• Page 101, line 9b:
  "row" should be "column".
  (Thanks to Shijia Jin!)
  
• Page 102, lines 16 and 24:
  "A_{21}" should be "A_{12}" (line 16), and "A_{12}" should be "A_{21}" (line 24).
  (Thanks to Shijia Jin!)
  
• Page 104, line 4b:
  The dimensions of the U submatrix should be (n-q) by q.
  (Thanks to Shijia Jin!)
  
• Page 129, Section 3.6.2.5:
  The section on Drazin inverses is irrelevant for any other material in the book. This section should be omitted or else moved to Chapter 8.
  
• Page 129, line 4b:
  instead of "for any positive integer k", should be
  "where k is the smallest nonnegative integer such that rank(A^(k+1))=rank(A^k)".
  (Thanks to Mirroslav Yotov!)
  
• Page 137, line 8:
  "disagonal", should be "diagonal".
  (Thanks to Zhilun Li!)
  
• Page 148, lines 17 and 20:
  "Hermitian" should be "unitary".
  (Thanks to Shijia Jin!)
  
• Page 180, Exercise 3.22(a) and 3.22(b):
  should include the statement "Let A be an idempotent matrix".
  
• Page 197, Table 4.1:
  The derivative of V(x) as given assumes the mean of x, xbar, is 0.
  The derivative in general is "2*(x - xbar/n)/(n - 1)".
  (Thanks to Kamesh Kompella!)
  
• Page 245, equation (5.30):
  This matrix is not an example of one that does not have a singular principal submatrix.
  The matrix in equation (5.20) is an example; also, see the first paragraph on page 246.
  (Thanks to Cássio Guimarães Lopes!)
  
• Page 379, equation (8.82):
  The last term should be raised to the power k.
  (Thanks to Richard Warr!)
  
• Page 427, line 1b, just after eq (9.49):
  Should be "The vectors v_i are the same..."
  (Thanks to Andres Velazquez!)