Math2331

Linear Algebra

Instructor: He Wang

he.wang@northeastern.edu

All course materials (homework/labs/tests/etc.) are on Canvas.

1.1 Introduction to Linear systems Math2331Sec1.1 (Homework: 1, 7, 10, 21, 24, 25, 36)

1.2 Matrices, Vectors, and Gauss-Jordan Elimination Math2331Sec1.2 (Homework: 2, 4, 5, 7, 18, 21-24, 31-33, 36, 37)

1.3 On The Solution of Linear Systems Math2331Sec1.3 (Homework: 1-8, 11-15, 21-31, 34, 36, 47, 55)

2.1 Intro. to Linear Transformations and Their Inverses Math2331Sec2.1(Homework: 1-3, 5, 6)

2.2 Linear Transformation in Geometry Math2331Sec2.2 (Homework: 1, 4, 6, 7, 8, 10, 19, 21,26abc, 53)

2.3 Matrix Products Math2331Sec2.3 (Homework: 3, 5, 11, 13, 16-23, 25, 29, 47)

2.4 The Inverse of a Linear Transformation Math2331Sec2.4 (Homework: 1-3, 5, 6, 17, 19, 35-41 (odd) )

3.1 Image and Kernel of a Linear Transformation Math2331Sec3.1 (Homework: 1, 3, 5, 7, 12, 15, 16, 23, 25, 33, 35,42)

3.2 Subspaces of Rn; Bases and Linear Independence Math2331Sec3.2 (Homework:1, 3, 11-33(odd), 26, 37, 39, 46, 49, 52)

3.3 The Dimension of a Subspace of Rn Math2331Sec3.3 (Homework: 1, 3, 5, 7, 11,13, 17, 21, 23, 27, 37, 39, 51 )

3.4 Coordinates Math2331Sec3.4

5.1 Orthogonal Projections and Orthonormal Bases Math2331Sec5.1 (Homework: 1, 3, 5, 15, 17, 27, 35)

5.2 Gram-Schmidt Process and QR Factorization Math2331Sec5.2 (Homework: 5, 7, 19, 21, 33, 35)

5.3 Orthogonal Transformations and Orthogonal Matrices Math2331Sec5.3 (Homework: 5-8, 13-17, 27, 29, 37)

5.4 Least Squares and Data Fitting Math2331Sec5.4 (Homework: 1, 5, 7, 17-25 (odd), 31-33)

6.1 Introduction to Determinants Math2331Sec6.1 (Homework: 1-11(odd) ,17, 27, 29-32)

6.2 Properties of Determinants Math2331Sec6.2(Homework: 1, 5, 6, 11, 13, 15, 30, 37-42. )

7.1 Diagonalization Math2331Sec7.1 (Homework: 1-7, 9, 15-21 (odd), 34)

7.2 Finding the Eigenvalues of a Matrix Math2331Sec7.2 (Homework: 1-13(odd), 16 )

7.3 Finding the Eigenvectors of a Matrix Math2331Sec7.3 (Homework: 1-13(odd) , 21 )

7.4 Dynamical Systems Math2331Sec7.4 (Homework: 1-7 (odd), 11, 17, 21, 25 )

8.1 Symmetric matrices Math2331Sec8.1

8.2 Quadratic forms Math2331Sec8.2

8.3 Singlar Value decomposition Math2331Sec8.3

Linear Algebra with Applications, 5th Edition, by Otto Bretscher.

Further advanced reading: Math5110 lecture notes.

Further reading: Introduction to Linear Algebra, Gilbert Strang, Wellesley-Cambridge Press