Errata for Optimization Algorithms on Matrix Manifolds

If you find an error that is not in the list below, please let us know about it.

P.-A. Absil, R. Mahony, & R. Sepulchre

• page 43, line 15: "T_{\bar{x}}\mathcal{M}" should be "T_{\bar{x}}\bar{\mathcal{M}}".
• page 68, line 13: "\delta>0" should be "\delta\in(0,\epsilon)".
• page 86, Algorithm 3, step 2: "Y^T" is missing in -Y(Y^TY)^{-1}Y^TAY.
• page 123, line -6: "span(V)" should be "the orthogonal complement of span(V)".
• page 152, line -2: replace "minimizing geodesic" by "geodesic in $\mathcal{V}$".
• page 153, second line of the proof of Lemma 7.4.8: replace "grad f(v)" by "grad f(x)".
• page 171, equation (8.4): replace x^T(0) by u^T (in the middle term).
• page 174: at the end of the page, add: provided that the right-hand side is a bona-fide horizontal lift. Since horizontality is guaranteed by construction, it remains to require that $\mathrm{D} \pi (\bar{x}+\bar\eta_{\bar{x}}) [\mathrm{P}^h_{\bar{x}+\bar\eta_{\bar{x}}} \bar{\xi}_{\bar{x}}]$ does not depend on the choice of $\bar{x}$ in the fiber $\pi^{-1}(x)$. Equivalently stated, for all real-valued functions $f$ on the quotient manifold, $\frac{\mathrm{d}}{\mathrm{d}t} f( \bar{x}+\bar\eta_{\bar{x}} + t \mathrm{P}^h_{\bar{x}+\bar\eta_{\bar{x}}} \bar{\xi}_{\bar{x}} )|_{t=0}$ must not depend on the choice of $\bar{x}$ in the fiber $\pi^{-1}(x)$.
• page 179, line -15: "for all p" should be "for all \eta".
• page 181, line 6: remove the minus sign in the formula of alpha_k. (Observe that r_k is defined as b-Ax_k.)
• page 185, line -8: replace "\langle \xi, (DF (x))^* [F (x)] \rangle" by "g(\xi, (DF (x))^* [F (x)])".
• page 189, line 4: n rows
• page 196, line -4: D qf(X)[Z] = Q \rho_{skew}(Q^TZR^{-1}) + (I-QQ^T)ZR^{-1}