Advanced Analytics -- Linear Algebra: Homework

$Carl Meyer$

Advanced Analytics 591B: Linear Algebra

Homework Problems --- By Section Number In The Text Book

Lesson 1 (Wed 8/19): Linear Equations

1.2 Gaussian Elimination And Matrices, 1---5, 16
1.3 Gauss-Jordan Method, 1---3
2.1 Row Echelon Form And Rank, 1---4
2.2 The Reduced Row Echelon Form, 1---3
2.3 Consistency Of Linear Systems, 1---7
2.4 Homogeneous Systems, 1---6
2.5 Nonhomogeneous Systems, 1---6
Lesson 2 (Mon 8/24): Numerical Practicalities

1.5 Making Gaussian Elimination Work, 1---3, 7
1.6 Ill-Conditioned Systems, 1, 2, 4

Lesson 3 (Wed 8/26): LU Factorization & Vector Spaces

3.9 Elementary Matrices And Equivalence, 1---6
3.10 The LU Factorization, 1---3, 8, 9, 10
4.1 Spaces And Subspaces, 1---9
Lesson 4 (Mon 8/31): Fundamental Subspaces

4.2 Four Fundamental Subspaces, 1---6, 9 11, 12, 13
4.3 Linear Independence, 1---7, 9, 10, 11
4.4 Basis And Dimension, 1---6, 8, 9, 16
4.5 More About Rank, 1---8, 9, 16, 20

Lesson 5 (Wed 9/2): Norms & Least Squares

5.1 Vector Norms, 1---6
4.6 Classical Least Squares, 1---4, 6, 9, 10
Lesson 6 (Wed 9/9): Orthogonality & Eigenvalues

5.4 Orthogonal Vectors, 1---7, 9, 10, 12---14
7.1 Elementary Properties Of Eigensystems, 1---3, 5---7, 8, 10
7.2 Diagonalization by Similarity Transformations, 1---6,

Lesson 7 (Mon 9/14): Eigensystems Continued

7.5 Normal Matrices, 1---4,
7.6 Positive Definite Matrices, 1, 4---6
5.12 Singular value Decomposition, 1, 2

			Lesson 1 (Wed 8/19): Linear Equations 1.2 Gaussian Elimination And Matrices, 1---5, 16 1.3 Gauss-Jordan Method, 1---3 2.1 Row Echelon Form And Rank, 1---4 2.2 The Reduced Row Echelon Form, 1---3 2.3 Consistency Of Linear Systems, 1---7 2.4 Homogeneous Systems, 1---6 2.5 Nonhomogeneous Systems, 1---6				Lesson 2 (Mon 8/24): Numerical Practicalities 1.5 Making Gaussian Elimination Work, 1---3, 7 1.6 Ill-Conditioned Systems, 1, 2, 4

			Lesson 3 (Wed 8/26): LU Factorization & Vector Spaces 3.9 Elementary Matrices And Equivalence, 1---6 3.10 The LU Factorization, 1---3, 8, 9, 10 4.1 Spaces And Subspaces, 1---9				Lesson 4 (Mon 8/31): Fundamental Subspaces 4.2 Four Fundamental Subspaces, 1---6, 9 11, 12, 13 4.3 Linear Independence, 1---7, 9, 10, 11 4.4 Basis And Dimension, 1---6, 8, 9, 16 4.5 More About Rank, 1---8, 9, 16, 20

			Lesson 5 (Wed 9/2): Norms & Least Squares 5.1 Vector Norms, 1---6 4.6 Classical Least Squares, 1---4, 6, 9, 10				Lesson 6 (Wed 9/9): Orthogonality & Eigenvalues 5.4 Orthogonal Vectors, 1---7, 9, 10, 12---14 7.1 Elementary Properties Of Eigensystems, 1---3, 5---7, 8, 10 7.2 Diagonalization by Similarity Transformations, 1---6,

			Lesson 7 (Mon 9/14): Eigensystems Continued 7.5 Normal Matrices, 1---4, 7.6 Positive Definite Matrices, 1, 4---6 5.12 Singular value Decomposition, 1, 2