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 |
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| 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 |
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| page 53 | Line after (3.13): i = l(t-hat) should be i = l_1(t-hat) | 09/06/2013 |
| Chapter 5 | 2 x 2 Linear Systems | Posted |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 right-handed 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 |
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| 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 |
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| 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 |