R.W.Kaye and R.A.Wilson - Linear Algebra

Linear algebra, by R.W.Kaye and R.A.Wilson, can be obtained from all good bookshops, or from the publishers, Oxford University Press as a paperback (ISBN 0198502370) or hardback (ISBN 0198502389).

From the review in the Mathematical Gazette, March 1999:
`Familiarity is apt to dull the senses when reviewing mainstream texts such as this one, but make no mistake, this is a clearly and carefully written book that lecturers could easily lecture from and learners readily learn from: it merits a wide circulation.'

From the review in the Nieuw Archief voor Wiskunde, July 1999:
`... this book can be strongly recommended.'

Corrections

The following errors and misprints have already been found. If you have found any others, please email me at R.W.Kaye AT bham.ac.uk.

• p. 10: the top right entries in the inverse of A on lines 4 and 6 should be -5/4 not -5/2.
• p. 12: in the equation for the expansion of a determinant by its top row the entries a_1n in the second row, and in the top row of the first two subdeterminants, should be a_2n, and in the last subdeterminant, a_{1 n-1} should be a_{2 n-1}.
• p. 67: the base change in Example 4.13 has been done in the wrong order. There is a pdf file and a postscript file containing a corrected version.
• p. 72: in Exercise 4.6, the last occurrence of f₁ should read f₃.
• p. 88: in the definition of v_S replace the coefficients of the u_j by their complex conjugates (equivalently, swap v and u_j in this inner product).
• p. 91: in line 12, replace P_n-1 by P_n-1(x). Similarly in line 14, replace P_n by P_n(x)
• p. 115: in the line beginning P^T = ..., the last entry of the first matrix should be 1/sqrt(11), not sqrt(11).
• p. 117: in line 15, the second partial derivative should be dF/dy not dF/dx.
• p. 121: in Proposition 7.24, add 'Hermitian matrix over' after 'or' in first line. Also add ', minus the number of i < n such that D_i, D_i+1 have different sign' at the end of the statement.
• p. 140: in Exercise 8.4, replace -y+3z by -y-2z in the definition of f.
• p. 157: the second line of P^-1 should be negated.
• p. 160: in line 14, it is not true that (A-lambda_nI)e_n = 0. In fact it is a linear combination of e₁, ..., e_n-1. Thus the induction still works, but the proof needs some slight adjustments. There is a pdf file and a postscript file containing a corrected version.
• p. 184: P = (3 1;1 -1), not (3 -1;1 -1).
• p. 186: in Exercise 12.8(a), 4x_n should read 4y_n.
• p. 209: in line 3, read v₂ = v₃ = ... = v_k = 0, so that v = (1,0,...,0)^T.
• p. 226: remove the minus sign from -ih in line 10 (twice) and line 14.

Contact addresses

Dr. R.W.Kaye (Senior Lecturer in Pure Mathematics)
School of Mathematics and Statistics
The University of Birmingham
Edgbaston
Birmingham B15 2TT
U.K.

Prof. R.A.Wilson (Professor of Pure Mathematics)
School of Mathematical Sciences
Queen Mary, University of London
Mile End Road
London E1 4NS
U.K.

Last updated 2nd January 2012.