# Functions of Matrices: Theory and ComputationErrata

• Page 3, (1.4): there is an unwanted right parenthesis in the (1,m_k) position.
• Page 4, line 6: replace E_k by N_k.
• Page 10, second paragraph of Section 1.2.6: $\psi(t)$ is the minimum polynomial for $n>5$ but not for $n=4$, because $F_4$ has a repeated eigenvalue 1.
• Page 27, line -8: replace "it" by "its".
• Page 31, Problem 1.33: the displayed matrix should have an extra superdiagonal of 1s inserted immediately above the main diagonal, so that $$A = \left[ \matrix{ 1 & 1 & \frac{1}{2!} & \frac{1}{3!} & \dots & \frac{1}{(n-2)!} \cr & 1 & 1 & \frac{1}{2!} & & \vdots \cr & & 1 & \ddots & \ddots & \vdots \cr & & & \ddots & \ddots &\frac{1}{2!} \cr & & & & \ddots & 1 \cr & & & & & 1 \cr }\right]$$.
• Page 80, line 1: should read "[0/0], [1/1], [2/2], ...".
• Page 86: In lines 1 and 2 of Algorithm 4.14, n should be m, where T is block m-by-m.
• Page 97, last displayed equation should read $$\norm{E_k} \le c \norm{E_0} + c \norm{E_{k-1}} c \sum_{i=1}^{k-1} o( \norm{E_{k-1-i}} ) \le c \norm{E_0} + (1+(k-1)c) \cdot o( \norm{E_0} ).$$
• Page 102: in (4.37), and three lines below it, $f(\rho(A))$ should be replaced by $\max_i |f(\lambda_i)|$.
• Page 114, line 6: remove the period inside parentheses and replace "It" by "it" on the following line.
• Page 120, line 5: should read "the $\lambda_i$ are".
• Page 160, line -14 should read "if $A$ is a nonsingular $M$-matrix with $0< a_{ii} \le 1$ for all $i$ then all the iterates $X_k$ (or $Z_k$ in the case of iteration (6.19)) have the same properties.
• Page 165, line -3: $u_{ij} = {n-i+1 \choose n-j+1}$ should read $u_{ij} = {n-i \choose n-j}$.
• Page 161, Theorem 6.10 should say "A\in\mathbb{R}^{n\times n}" and the sentence before the theorem should say "real $H$-matrices".
• Page 217, line -3: the parentheses should read ("Berberian's trick").
• Page 224, line 9 of Algorithm 9.4 should read \omega_{s+1+r} and on line 10 add, just before "quit", "F = F_s".
• Page 222, line 9: $M^n=0$ should read $N^n=0$.
• Page 228, in line 6 of Algorithm 9.6 i should be j; in line 8 of Algorithm 9.6 j should be i.
• Page 234, Table 10.1: formula in (3,2) position should read $Q e^T Q^*$.
• Page 246, line 7: the first right parenthesis after $I$ should be deleted.
• Page 247, third line above Theorem 10.21: "scaling" should read "squaring".
• Page 253, line 2: "larger" should read "smaller".
• Page 261, in the first line of Section 10.7.3 a space is needed after "single shift".
• Page 265, Problem 10.6 should read "cond_abs(exp,A)".
• Page 266, Problem 10.16 should read "rounding errors in the squaring phase".
• Page 272, second display from bottom: on left-hand side, $\kappa_{\log}(A)$ should read $\mathrm{cond}_{\mathrm{rel}(\log,A)$.
• Page 274, line 8 should read "$m$-point Gauss-Legendre quadrature rule"
• Page 275, line -10: extra right parenthesis needed before the final "|".
• Page 280, line 1: the U should be in the mathcal font.
• Page 283, line 11 of Algorithm 11.12: $L = 2G_0$ should read $L = 2G_1$.
• Page 283, 7 lines before Section 11.9: should read "Algorithm 11.2 can be combined".
• Page 330, line 5: should read "on Hermitian matrices".
• Page 332, 9 lines before Section B.16: should read "a complex addition requires 2 real additions".
• Page 333, in equation (B.25) a right parenthesis should be added after $x_{j-1}$.
• Page 336:
• delete the "LU" line (appears in Table C.2).
• HM line should read "$2n^3$".
• TY = B line should read "$n^3/3$".
• HY = B line should read "$5n^3/3$".
• Page 370, in solution to Problem 8.26, in (b) the operation count for (8.37) should be $3mn^2 + n^3/3$.