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!*)

Thanks also to Mirroslav Yotov for additional general comments.