Math 4031 Linear Algebra

Catalog Description

Three credits. Three hours of lecture per week. Prerequisite: MATH 3151.

Matrix algebra. Determinants. Systems of linear equations. Finite dimensional vector spaces. Linear dependence and independence. Bases. Euclidean spaces. Linear transformations. The matrix of a linear transformation. Similarity transformations. Eigenvectors and eigenvalues. Inner products. Norms. Orthogonal projection. Gram-Schmidt orthogonalization.

• Generic Course Objectives
• Classroom Behaviour
• On the use of electronic aparati
• In Praise of Lectures

2018-2019– Semester II

Miscellaneous Notes

1. Matrix Multiplication
2. Elimination and Back Substitution.
3. The Inverse of a Matrix.
4. LU Factorization.
5. Permutations and Transpositions
6. Reduction to the Identity
7. Linear Spaces
8. Linear Independence
9. Euclidean Space
10. Lines in Euclidean Space
11. Gram Schmidt Algorithm
12. Orientation in $R^2$
13. The Vector Product
14. Planes
15. Linear Equations
16. Linear Equations – Simple Examples
17. Subspaces (updated April 27 2019)
18. The Hermite Normal Form
19. Matrix of a Linear Map
20. Dimensions of Kernel and Image 
21. The Null Space of a Matrix
22. Finding the Left Nullspace
23. The Jordan Normal Form
24. Determinants.
25. Determinant of a Direct Product.
26. Graph Matrices
27. Circuits
28. Closure
29. Affine Spaces in Physics
30. Distance to an Affine Subspace
31. Convex Sets
32. The Centroid
33. Projection and Least Squares

Homework

1. Homework on Matrices.
2. Homework on Elementary Matrices and LU Factorization.H
3. Homework on Geometry

Texts

1. Lang, Serge, Introduction to Linear Algebra, Springer, 1997.
2. Gilbert Strang, Introduction to Linear Algebra, Ed. 4, 2009.

Bibliography

1. Gilbert Strang, Introduction to Linear Algebra, Ed. 4, 2009.
2. David Santos, Linear Algebra Notes, 2010.
3. Sheldon Axler, Linear Algebra Done Right, Springer, 1997.
4. Sergei Treil, Linear Algebra Done Wrong.
5. E. D. Nering, Linear Algebra and Matrix Theory , Wiley, 1970.
6. I. Satake, Linear Algebra, M. Dekker, Inc., New York, 1975.
7. G. E. Shilov, Linear Algebra, Dover Publications, New York, 1977.
8. Lang, Serge, Linear Algebra, Addison Wesley, 1968.
9. Peter D. Lax, Linear Algebra and Its Applications, 2nd Edition, 2007.
10. I. M. Gelfand, Lectures on Linear Algebra, Dover 1989 (translation).
    

Online Tools and Video Resources

1. Multipurpose Calculator
2. Online Lectures from MIT by Gilbert Strang.
3. Linear Algebra Toolkit