# Math for Data

Mathematical Foundations for Data Analysis

# Errata

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• page 3 : line 14 should have condition “0.1 <= y <= 0.6” instead of “0.1 <= 0.6” in the definition of set B.

• page 43 : vector v should be [v1;…;vd] h/t Bolin Chen

• page 46 : “Example: Adding Vectors” -> “Example: Adding Matrices” h/t Bolin Chen

• page 47 : The last sentence in example box, “upper right corner” should be “upper left corner” h/t Bolin Chen

• page 54 : in Example box: “eigenvector \lambda_2” should be “eigenvalue \lambda_2” h/t Bolin Chen

• page 54 : the determinant section: the vectors b-a and d-c should be (b,a) and (d,c) h/t Bolin Chen

• page 64 : second paragraph of 4.2.3: d_cos(A,B) should be d_cos(alb) h/t Bolin Chen

• pages 73, 151, 244 : A code block invokes “SciPy” when it should invoke “scipy” with all lower case letters.

• page 84 : the second paragraph of 4.6.3 should discuss “false negatives” not “false positives” h/t Bolin Chen

• page 104 : last element of y should be y_n not v_n h/t Bolin Chen

• page 108 : the right term of SS_{reg} should be ||r||^2 h/t Bolin Chen

• page 117 : the first X_6^T in the third paragraph should be X_4^T h/t Bolin Chen

• page 148 : “non-decreasing” should be “non-increasing” h/t Bolin Chen

• page 154 : For matrices U, V from the SVD the book states the Frobenious norm of these matrices is 1 (that is, ||U||_F=1 and ||V||_F=1). It should state the spectral norm is 1 (that is, ||U||_2=1 and ||V||_2=1), and point out they are norm-preserving under multiplication. h/t David R. Gurney

• page 156 : the formula on the bottom should have sigma_j^2 instead of sigma_i^2 h/t Bolin Chen

• page 156 : footnote: “the right n-d rows of U” should be “the right n-d columns of U” h/t Bolin Chen

• page 160 : the “top k right singular values V_k” should be “top k right singular vectors V_k” h/t Bolin Chen

• page 163 : Let E_i be an nxn matrix that is all 0s except the ith column which is all 1s, and Z an nxn matrix. The books states E_i Z has each column as the ith column of Z, and Z E_i^T has each row as the ith row of Z. It should almost be the reverse where E_i Z has each row as the ith row of Z, and Z E_i^T has each row as the ith column of Z. h/t David R. Gurney

• page 182 : “k-mediod” should be “k-medoid” h/t Bolin Chen

• page 243 : Ergodic Markov Chains box should have q_* not q^* h/t Bolin Chen

• page 252, 254 : different implementation of the eigen-decomposition give somewhat different outputs for laplacians L_0 and L in the examples. These are computed with octave’s eig function. Moreover, an eigenvalue/eigenvector pair is missing for the decomposition of L_0. h/t Bolin Chen

• page 263 : second last line has an extra “m’+1” h/t Bolin Chen

• page 272 : Algorithm 11.2.4 should say “Count Sketch” not “Count-Min Sketch” h/t Bolin Chen

• page 272 : the last formula “C_{i,h_i}(q)” should be “C_{i,h_i(q)}” where (q) is in the subscript. h/t Bolin Chen

• page 274 : the second to last paragraph should say “the eigenvalues of C are the squared singular values of A” not “of C” h/t Bolin Chen