Professor Alexandru I. Suciu

MTH 1230 - Linear Algebra

Spring 2001

* Course Information

Course: MTH 1230, Linear Algebra   (Seq. 10, Sec. 02, Key #02367)
Instructor: Prof. Alex Suciu
Course Web Site:    www.math.neu.edu/~suciu/mth1230/linalg.sp01.html
Time and Place: Tue., Wed. & Fr., 11:45 AM -- 12:50 PM, in 302 KA
Office Hours: Tue., Wed. & Fr., 10:40 AM -- 11:40 AM, in 441 LA
Prerequisites: MTH 1223 (Calculus for Engineering majors 4) and MTH 1225 (Differential Equations 1) or equivalent
Textbook: Linear Algebra with Applications Second Edition, by Otto Bretscher, Prentice Hall, 2001
Grade: 60% in-class exams, 40% final exam

* Course Objective

This course is an introduction to concepts, algorithms, theory, and applications of Linear Algebra. This subject is now recognized as being fully as important as Calculus in its range of applications.

The course begins with methods for solving a system of linear equations in several unknowns. We will also learn how to find an approximate solution when no tru solution exists. We then proceed with the study of linear transformations and matrix operations, subspaces of n-dimensional space, images and kernels, bases and linear independence, orthonormal bases and QR-factorizations, with applications to least squares and data fitting. The course ends with a study of eigenvalues and eigenvectors, and uses these concepts to model change via difference equations. A further application of these ideas is the singular value decomposition of a matrix, which is useful in transmission of information.

* Homework Assignments

Section Problems
1.1: Linear systems and their geometry 1, 7, 10, 20--22, 34
1.2: Matrices & Gaussian elimination 2, 4, 5, 7, 17, 18, 20--22, 27, 29--31, 34, 35, 37, 41, 42
1.3: Solutions and matrices 1--8, 10-15, 17--19, 21--32, 34--36, 47, 55
2.1: Linear transformations, inverses 1--3, 5, 6, 9, 11, 24--30, 33, 35, 42
2.2: Geometry of linear transformations 1, 3, 4, 6--10, 17, 19, 21, 23--26, 34, 43, 49
2.3: The inverse of a linear transformation 1--5, 17, 19, 25, 35--41
2.4: Matrix products 1--25 (odd only), 29, 47, 48, 49, 65, 76, 78
3.1: Subspaces, images and kernels 1, 3, 5, 7, 10, 14, 15, 23, 25, 33, 35, 42, 53, 54
3.2: Bases and linear independence 1, 3, 11--33 (odd only), 24, 37, 39, 46, 49, 52
3.3: Dimension of a subspace 1, 3, 5, 7, 11, 13, 17, 21, 23, 27, 37, 39, 49, 52
5.1: Orthonormal bases and projections 1, 3, 5, 13, 15, 17, 27, 31
5.2: Gram-Schmidt process & QR-factorization 5, 7, 19, 21, 33, 35
5.3: Orthogonal matrices 5--8, 13--18, 27--29
5.4 Least squares & data fitting 8, 11, 13, 17--25, 31--33
6.1 Determinants 1--11 (odd only), 17, 20, 27
6.2 Properties of determinants 1, 4--10, 24--26, 31, 32, 37
6.3 Geometry of determinants 2, 7, 9, 13, 14, 23
7.1 Eigenvectors, iteration of matices 1--7, 9, 15--22, 34
7.2 Finding eigenvalues 1--13 (odd only), 21, 28--31
7.3 Finding eigenvectors 1--13 (odd only), 21, 40, 42, 43
7.4 Diagonalization and similarity 1--9 (odd only), 18--22, 38--50
8.1 Symmetric matrices 1, 3, 7
8.3 Singular value decomposition 1--4, 17, 18

* Class Materials

* Grades

An finally, here are the grades!

  Department of Mathematics Office: 441 Lake Hall
  Northeastern University Phone: (617) 373-4456
  Boston, MA, 02115 Email: alexsuciu@neu.edu 

Home  Started:  March 27, 2001  Last modified:  June 7, 2001
URL:  http://www.math.neu.edu/~suciu/mth1230/linalg.sp01.html