# Errata

In a book of over 650 pages, produced under time pressure, some errata are perhaps unavoidable. We are nevertheless embarassed by any error, and apologize for any inconvenience caused.All we can do at this stage is report the errors we know about. We are interested in any you may find, to improve a possible second printing of our book. Please send them to leo@science.uva.nl. We have put time stamps on the corrections made since the appearance of the book, to facilitate updating your copy.

Below are the major corrections which you definitely want to fix in your copy.
A second page lists all corrections-minor corrections, improvements and obvious typos as well as the major.
We also have a page with *all* errata (major or minor) in reverse chronological order
of fixing.

*Not all browsers support all standard html symbols (older versions of Internet Explorer, for example). If you think that this symbol "*⌋*" looks like a square, you may want to view the bitmap symbol version.*

- Pg 49, first equation:
both indices should run from
*0 to n*. [20070411 AH] - Pg 49, equation (2.10):
Is wrong, it should count all contributions that make up the
intended grade, as in

<*A*∧*B*>_{k}= Σ∧^{k}_{i=0}<A>_{i}*<B>*._{k-i}

We do not actually use this Grassmann algebra equation, so this error does not affect the mathematics in the remainder of the text. [20070507 RP] - Pg 109, line 4: Only for a Euclidean metric with an orthonormal basis is the matrix of the adjoint equal to the transpose; for other metrics, a metric tensor needs to be included with the transpose. This fact makes the final statement of this paragraph all the more valid. [20071127 GG]
- Pg 137, structural exercise 2: The target formulas are wrong, and the exercise should be cancelled. [20080712 GG]
- Pg 190, the entry for row
**A**and column**Y**should have an extra (-1)^{n-1}. [20070401] - Pg 217, (8.3): coefficient 1/4 should be 1/3!. [20070822 AC]
- Pg 222, equation (8.8):
Implicitly, we have used that
**I**is constant in step 2 (where we use (exp(-**I**φ/2))' = (-**I**φ/2)' exp(-**I**φ/2) ), although the text claims that both**I**and φ can vary. The proper of the derivative of the versor*R*(τ) does result in a commutation product with a bivector. But this bivector is not ∂_{τ}[**I**φ], it is -2∂_{τ}[*R*(τ)]*R*(τ)^{˜}, which evaluates to**I**∂_{τ}[φ]+∂_{τ}[**I**](exp(**I**φ)-1)/**I**. (Use ∂_{τ}[exp(-**I**φ/2)] = ∂_{τ}[cos(φ/2)-**I**sin(φ/2)] = -**I**∂_{τ}[φ/2]exp(-**I**φ/2) - ∂_{τ}[**I**]sin(φ/2).) [20080712 PJ] - Pg 237, penultimate entry Table 8.2:
should be
*∂*P[-_{X}(X^{-1}*A) =*X*]. [20080326 RV]^{-1}A X^{-1} - Pg 253, (10.11):
exchange
**a**and**b**, and include a minus sign in all three definitions. This gives positive angles for a positive orientation of**a**∧**b**∧**c**. [20070822 AC] - Pg 254, first equation: swap
**a**and**c**. [20070822 AC] - Pg 291, Table 11.3:
entry Support of Finite Flat should have denominator
*e*_{0}^{-1}⌋*X*. [20070904 AC] - Pg 305, lines 10, 17 for
*X*^{*}: change*e*_{0}^{-1}to -*e*_{0}^{-1}[20070915 AC] - Pg 329, (12.3), and Table 12.1:
In earlier errata, we tried to bring our notation in agreement with at least one standard on the signs of Plücker coordinates, namely the often referred [57]. This is possible, but since [57] uses a counterintuitive characterization of the direction of the line PQ (namely from Q to P), the changes relative to our text are rather ubiquitous. For this edition of the book, the simplest is to distinguish between the 'Shoemake Plücker direction'
**a = p-q**, and the 'GA direction'**u = q-p = -a**. The moment vector**m = p × q**can be defined as**m**= (**p**∧**q**)^{*}. With that, the line of (12.2) would be represented in [57] as -{**a**,**m**}, so that is the change to (12.3). Though the line coordinates are homogeneous, an oriented geometry should process this sign consistently. But Table 12.1 is about the line {**a**,**m**}, oriented from Q to P, since [57] is.*Our great thanks to Allan Cortzen for helping to sort out these annoying signs!*[20080712 AC] - Pg 332, line -14 and corresponding line in Table 12.1 'Plane through line and point':
change -
**m**⋅**p**to**m**⋅**p**. [20080712 AC] - Pg 335, Table 12.2, entry (Affine,Plane):
Change -[
**t**]^{T}to -[**t**]^{T}det(f)[f]^{-T}, and change 1 (element [4,4]) to det(f). [20070915 AC] - Pg 389, structural exercise 1:
A
**p**is missing on the right hand side. [20070716] - Pg 407, Table 14.1:
Some annoying sign errors crept into this table and its associated
derivations. You may download a new
copy of the table with all these corrections incorporated.
[20070717]
- Table 14.1, entry (flat, direction): add minus
- Table 14.1, entry (dual flat, direction): add minus
- Table 14.1, entry (dual tangent, direction): change to
*(-∞*⌋*X*^{-*})∧ ∞ - Table 14.1, entry (dual round, direction): change to
*(-∞*⌋*X*^{-*})∧ ∞ - Table 14.1, entry (tangent, location): add minus to
*X/(∞*⌋*X)* - Table 14.1, entry (dual tangent, location): add minus to
*X/(∞*⌋*X)* - Table 14.1, entry (round, location): add minus to
*X/(∞*⌋*X)* - Table 14.1, entry (dual round, location): add minus to
*X/(∞*⌋*X)* - Table 14.1, entry (round, squared size): change minus to plus
- Table 14.1, entry (dual round, squared size): change plus to minus

- Pg 407, table 14.1: On top of other errors already corrected earlier, the entry (dual round, squared size) should have the plus changed to minus. [20071130 AC]
- Pg 408, line -9:
Remove "
*but the formula then computes -ρ*" [20070401]^{2} - Pg 409, line -8:
include minus sign in
*X/(∞*⌋*X)*[20070401] - Pg 472, line 6:
replace by
*T*_{t}*R*=*R**T*_{R-1tR}. [20071019 AH] - Pg 475, line -3:
The answer for this transversion over
**t**should be 1 +*o***t**=*e*^{ot}. This correction should be propagated through the text. It changes the last line of Table 16.1 (remove the '/2' twice), and the last column of Table 16.2 (replace**t**by 2**t**in this column only). [20080103 AC] - Pg 589, equation (B.1):
first
**B**⌋**A**on last line should be**A**⌊**B**[20071127 PJK]

We are very grateful to all who reported these errors, big and small!

In order of number of first reported and acknowledged errors, they are: The counts in this list include the minor errata.