errata
If you find errors in the text or figures, please report them to Dianne Hansford.
We will give you credit unless you request not to be named.
Chapter 1  Descartes' Discovery: 2D Lines  Posted 

page 12  Exercise 4: (min_1, min_2) should be (min_1, min_2, min_3) and (max_1, max_2) should be (max_1, max_2, max_3) Found by Jeff Griffin 
12/12/2013 
page 13  Exercise 7: (v_1, v_2) should be (1/2,0).  02/03/17 
Chapter 3  Lining Up: 2D Lines  Posted 

page 53  Line after (3.13): i = l(that) should be i = l_1(that)  09/06/2013 
Chapter 5  2 x 2 Linear Systems  Posted 

page 105  In Example 5.5, the following sentence in misleading. "In this example, any vector u that is perpendicular to a_1 will be projected to the zero vector." Actually, vectors perpendicular to the row vectors are mapped to the zero vector. In this example, the row vectors are identical to the column vectors. 
05/15/2021 
page 114  Example 5.9: Typesetting error in the line starting with A = V'V^{1}. The matrix V' is incorrect in this line. It should be [v'_1 v'_2], thus the first column is [1 1]^T and the second column is [1 1]^T Found by Tim at Univ of Colorado at Colorado Springs 
09/14/2015 
Chapter 7  Eigen Things  Posted 

page 144  Example 7.3: All references to r_1 should be r_2. This includes r_2,1 and r_1,1, which should be r_2,2 and r_1,2, respectively.  09/06/2013 
page 152  In the displayed equation for the matrix R, the element r_1,2 should be +0.3.  05/15/2021 
Chapter 8  3D Geometry  Posted 

page 175  Exercise 18: Let's be more specific. Let u_1 be the projection of w into the subspace defined by v  09/06/2013 
Chapter 9  Linear Maps in 3D  Posted 

page 185  First equation on page: v' = Sv should be v' = S_1v. On the next line, "An a_i,j element", is refering to an element of S_1 
09/06/2013 
Chapter 10  Affine Maps in 3D  Posted 

page 214  First paragraph of page: "The intersection point x is" should refer to x'  09/06/2013 
page 217  Bottom pf page: "transfomation" is missing an "r"  09/06/2013 
page 219  The matrix following (10.10) would be better written with the last row as [n_1 n_2 n_3 0]. This would match the pipeline structure of sending one projection matrix for all vertices. Also, this matrix will act on homogeneous points and vectors, whereas the version in the text operates on points only. Found by Christoph Fuenfzig 
02/26/2018 
Chapter 13  Alternative System Solvers  Posted 

page 287  Equation (13.8): v should be v  09/26/2013 
page 299  Misspelling of involutory in Exercise 2 and WYSK. This also occurs on pages 281, 284, and in the index. Found by Radu Grosu 
05/11/2016 
Chapter 14  General Linear Spaces  Posted 

page 306  In Example 14.5, the vector v_2 should be [5 0 6 1]^T  05/15/2021 
page 306  In Example 14.6, the vector v_3 should be [3 4 3]^T  05/15/2021 
page 314  In the construction of Pv, each term should be divided by
<u_j,u_j > for j=1,...,k. For example, the first term should be <v,u_1 > u_1 / <u_1,u_1 > 
05/15/2021 
page 315  Bottom of page: Equation for b_4 is missing . in the denominator; however, the solution is correct because the normalization was done. . = sqrt(1/2) 
09/26/2013 
page 316  Section 14.5 example of polynomials of fixed degree n: We consider all polynomials of degree < n to be of degree n. Instead of "fixed degree n" we could have said "of degree less than or equal to n" Found by Raud Grosu 
05/11/2016 
Chapter 15  Eigen Things Revisited  Posted 

page 330  At the top of the page, in the conclusion to Example 15.7, r = 1r_2 + 1r_3. 
05/15/2021 
page 331  For the basic power method presented here, we assume that the matrix A has n distinct eigenvalues, thus in the second sentence it should read lambda_1 > lambda_2  05/15/2021 
page 341  Two occurances of r^(1) = [1 1 1] should be r^(1) = [1 1 1]^T  09/26/2013 
page 335  Figure 15.3 should have an arrow from node 4 to node 3.  04/30/2015 
Chapter 16  The Singular Value Decomposition  Posted 

page 347  Matrix V displayed near the top of the page is actually V^T Found by T. Boult 
12/17/2018 
page 347  The previous errata entry should be ignored. The actual error is in the display of V^T in the middle of the page. In error, V is given in the matrix product.  5/15/2021 
page 353  "A note on U: ... eigenvectors A^TA" should state "A note on U: ... eigenvectors AA^T" Found by Radu Grosu 
05/11/2016 
page 366  Exercise 17: The second column of the matrix X should be 2, 1, 0, 1, 2, 1, 1 to match the given solution. Found by Radu Grosu 
05/11/2016 
page 366  Correction to previous correction! Exercise 17: The second column of the matrix X should be 2, 1, 0, 1, 2, 1, 1 to match the given solution. Found by Javier Cano 
04/10/2021 
Chapter 20  Curves  Posted 

page 413  There are 51 points generated by t=0, 1/50, ..., 1 Found by Seth Kingsley 
12/17/2018 
page 425  Last paragraph, bottom of page: equation f_2 = f_1 \wedge f_3 should be f_2 = f_3 \wedge f_1. (See page 426 erratum for explanation.)  09/26/2013 
page 426  Equation (20.18): should be f_2 = f_3 \wedge f_1. Convention has it that f_2 has the same orientation with respect to the curve as the second derivative. This ideas is expressed in Sketch 20.9. Also, convention has it to create a righthanded local frame. 
09/26/2013 
page 428  Exercise 10: attach the curve c(t) at d(0) = d_0.  09/26/2013 
Appendix B  Selected Exercise Solutions  Posted 

page 444  Exercise 4: (v_1, v_2, v_3) closing parenthesis is missing  09/06/2013 
page 446  Exercise 28: solution should be [3 2]^T  0.5*[1 1]^T = [5/2 5/2]^T Found by Seth Kingsley 
02/26/2018 
page 448  Exercise 27: The last equation should be m(t) = [2 3/2]^T + t[1 4]^T Found by Temaran 
07/01/2016 
page 453  Exercise 8: "is mapped to x=" should be "is mapped to x' ="  09/06/2013 
page 455  Exercise 12: Incorrect article for "an hyperboloid" and "an paraboloid"  09/06/2013 
page 462  Exercise 2: The question asked for an affine map; it is p' = A(p  x_1) + y_1 In this exercise, Ax_1 = Ay_1, thus the affine map is really just a linear map (a reflection). 
09/06/2013 
page 465  Exercise 10: The solution given is for v = [1/3 1/3 2/3]^T and n = [0 0 1]^T. For v and n in the problem definition, v' = [1/3 2/3 2/3]^T + 2/3[1 0 0 ]^T = [1/3 2/3 2/3]^T Found by Temaran 
07/02/2016 
page 482  Exercise 1: In the matrix, the lambda=1. Therefore, the circle is x^Tx  r^2 = 0. 
09/06/2013 
page 483  Exercise 4: Delete the last sentence of the solution. (The rotated ellipse was already given at the beginning of the solution.)  09/06/2013 
page 484  Exercise 15: The given scaling is incorrect. The circle with with center at the origin and radius 2 is mapped to the ellipse with x_1 extents +/ 1/sqrt(2) and x_2 extents +/ 1/2 by the scaling matrix with diagonal elements s_11 = 1/(2sqrt(2)) and s_22 = 1/4. Found by Radu Grosu 

page 483  Exercise 9: The definition of D is incorrect. The 4 should be a 2.  09/06/2013 
page 485  Exercise 5: To complete the solution, we should add "thus the monomial form is a_0 + ta_1 + t^2a_2 + t^3 a_3" 
09/06/2013 
page 486  Exercise 8: f_2 and f_3 are incorrect. f_3 = [0 0 1]^T and f_2 = [0.99 0.14 0]^T 
09/06/2013 
page 486  Exercise 10: The equation c_ 2 = c_0 + c[d_0  d_1] should be c_2 = d_0 + c[d_0  d_1] 
09/06/2013 