Instructor’s Solution Manual for “Linear Algebra and
Optimization for Machine Learning”
Charu C. Aggarwal
IBM T. J. Watson Research Center
Yorktown Heights, NY
March 21, 2021
,ii
,Contents
1 Linear Algebra and Optimization: An Introduction 1
2 Linear Transformations and Linear Systems 17
3 Diagonalizable Matrices and Eigenvectors 35
4 Optimization Basics: A Machine Learning View 47
5 Optimization Challenges and Advanced Solutions 57
6 Lagrangian Relaxation and Duality 63
7 Singular Value Decomposition 71
8 Matrix Factorization 81
9 The Linear Algebra of Similarity 89
10 The Linear Algebra of Graphs 95
11 Optimization in Computational Graphs 101
vii
, viii
Optimization for Machine Learning”
Charu C. Aggarwal
IBM T. J. Watson Research Center
Yorktown Heights, NY
March 21, 2021
,ii
,Contents
1 Linear Algebra and Optimization: An Introduction 1
2 Linear Transformations and Linear Systems 17
3 Diagonalizable Matrices and Eigenvectors 35
4 Optimization Basics: A Machine Learning View 47
5 Optimization Challenges and Advanced Solutions 57
6 Lagrangian Relaxation and Duality 63
7 Singular Value Decomposition 71
8 Matrix Factorization 81
9 The Linear Algebra of Similarity 89
10 The Linear Algebra of Graphs 95
11 Optimization in Computational Graphs 101
vii
, viii
