Matrix Algebra: Theory, Computations and Applications in Statistics

Errata and Clarifications

• Page 19, line 3 (the second bullet):
  the expression after the second "equals" mark should be "|a|(\sum c_i^2)^1/2"; that is, the a^2 within the summation should be deleted.
  (Thanks to Rory Michaelis!)
  
• Pages 19 through 25 in five displayed equations (two on p. 19, two on p.20 one of which has multiple lines, and one on p. 25):
  all index initializations should be "i=1" (instead of "1=i" or even "1=1" in one case!). And I thought that I used "copy-and-paste" to reduce the number of errors!
  (Thanks again to Rory Michaelis!)
• Page 47, line 1:
  "elements" should be "element"
  
• Page 84, line 8b:
  "column row rank" should be "column rank"
  (Thanks to Greg Fodor!)
  
• Page 89, line 9b:
  "(xA)^T C(Ax)" should be "(Ax)^T C(Ax)"
  (Thanks again to Greg Fodor!)
  
• Page 90, line 3b:
  "(yA)^T (Ay)" should be "(Ay)^T (Ay)"
  (Thanks again to Greg Fodor!)
  
• Page 93, prior to equations (3.133) through (3.139):
  add the condition "and such sums as I+A, A+B, and so on, are full rank" (that is, every matrix whose inverse is indicated is of full rank).
  also on page 93, line 5 from the bottom, should say
  "... these equations may hold ..." (also see correction for page 101 below)
  (Thanks to John Angus!)
  
• Page 101, Section 3.6.1:
  should say
  "Equations (1.133) through (1.139) do not hold in general."
  (Thanks again to John Angus!)
  
• Page 128, line 3:
  The matrix D should be n by n, rather than "m by m"
  (Thanks again to Greg Fodor!)
  
• Page 154, Table 4.1:
  the derivative of ax should be "aI";
  the derivative of xx^T should be "x K I + I K x", where "K" denotes Kronecker product.
  (Thanks to Chetan Bhole!)
  The definition of the derivative of a matrix Y with respect to a matrix X given in equation (4.15) on page 155 is the common definition used by statisticians. It might be noted that an alternate and perhaps better definition is
  dY/dX=d(vec(Y))/d(vec(X)).
  
• Page 159, line 6b:
  "m X m-k" should be "m X (m-k)"
  (Thanks to Chu Xinqi!)
  
• Page 174, line 21:
  "(xQ)^T (Qy)" should be "(Qx)^T (Qy)"
  (Thanks again to Greg Fodor!)
  
• Page 180, lines 5 and 15:
  "u" should be "v"; that is, the reflection is about v
  (Thanks to Eric Arora!)
  
• Page 226, line 1b:
  There should be a final factor of Q'; that is, the equation should be
  X^+ = [R_1^{-1} 0]Q^{\rm T}
  (Thanks again to Greg Fodor!)
  
• Page 236, line 9:
  should say "sufficient condition for a unique solution to exist is that d_{m}>d_{m+1}. (Recall ..."
  If d_{m}=d_{m+1} a solution may or may not exist.
  
• Page 289, eq (8.48):
  should be "XB = XC" instead of "X^TB=X^TC".
  (Thanks to Wei Luo!)
  
• Page 340, line 12:
  "Beta_W" should be "Beta_V".
  (Thanks to Jaafar AlMutawa!)
  
• Page 343, eq (9.32):
  the gamma should be transposed
  (Thanks to Hal Pedersen!)
  
• Page 350, Section 9.4.5:
  The statistic (9.49) generally does not have a chi-squared distribution, as pointed out by Cragg and Donald (1996, JASA v. 91, 1301). (This is due to to the indeterminacy of the decomposition referred to in the paragraph following expression (9.49).) Cragg and Donald suggest an alternative test based on the LDU decomposition. Another, likely better, test based on the SVD was proposed by Kleibergen and Paap (2006, J. Econometrics v. 133, 97).
  (Thanks to Majid Al-Sadoon!)
  
• Page 472, lines 3 and 4 from bottom:
  There should be two sentences:
  Hilbert matrices have large condition numbers; for example, the $10 \times 10$ Hilbert matrix has condition number of order $10^{13}$. The Matlab function {\tt hilb(n)} generates an $n \times n$ Hilbert matrix.
  (Thanks to chtoch!)
  
• Page 489, line4b:
  "diagonal" should be "trace"