Introduction This is the most classical origin of an important concept known as the condition number of a matrix. Our goal is to give a detailed view of different methods, because while this is a well-known topic there are several techniques and few standard presentations of total rigor. [IN PROGRESS NOTE] Absolute Condition The absolute condition number of matrix inversion with respect to a particular norm, $\|\cdot\|$, is given by the formula, ...

Introduction This list is neither complete, nor official. This is intended to be a collection of errors or confusions found throughout my occasional skimming of this book. Further errors can be contributed from others, and will be appropriately credited. Jim has an errata posted on the course page of Math221 : Numerical Linear Algebra at UC Berkeley. Things added here deliberately omit previously known remarks. Errata Pg. 20, 78, 151 all refer to the “Cauchy-Schwartz” inequality, when it is more commonly Cauchy-Schwarz. It appears this is not a case of multiple transliterations of a name such as Chebyshev whose name finds many spellings. Also pages 353-356 use Schwarz when referring to the additive Schwarz method, so at minimum the same Hermann Schwarz’s name has been given two distinct spellings. Pg. 27 Question 1.17, $fl\left(\sqrt{x^2}\right) = x$ should read $fl\left(\sqrt{x^2}\right) = \left| x \right|$ Pg. 51 Fig. 2.2 caption omits machine epsilon, $\varepsilon$, for $+$. Pg. 51 Fig. 2.2 caption uses $x$ instead of $\hat{x}$ for the third relative backward error bound annotated by $\circ$. Pg. 96 the formula for scaled backward error uses $\|x\|$ instead of $\|\hat{x}\|$. See Theorem 7.1 (Rigal and Gaches) in Higham’s ASNA. In addition, scaled backward error picks up an extra division by machine epsilon when referenced as $R/\varepsilon$. Possible Clarifications For anyone cross-reading “Introduction to Matrix Computations” by Golub and Van Loan, Demmel’s machine epsilon is their unit roundoff.

Introduction This list of errors is not complete, nor official. This is intended to be a collection of errors found throughout my occasionally skimming of this book. Further errors can be contributed from others, and will be appropriately credited. The link to the books errata given in the front matter appears to be dead, so it is possible many of these have been discovered by prior readers. Errata Pg. 115, the Matrix $A$ uses $v$ for the latter $n-1$ elements of the first column while the subsequent analysis uses the letter $z$. Either $A$ needs to use $z$ or the subsequent uses of $z$ need to be replaced with $v$. ...