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

by James E. Gentle

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 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 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 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 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!)