#### 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.

### 2018-2019– Semester II

- Syllabus
- Lecture Notes
- Generic Course Objectives
- Classroom Behaviour
- On the use of electronic aparati
- In Praise of Lectures
- UPR Regulations concerning Academic Integrity and Reasonable Accommodation”

#### Miscellaneous Notes

- Matrix Multiplication
- Elimination and Back Substitution.
- The Inverse of a Matrix.
- LU Factorization.
- Permutations and Transpositions
- Reduction to the Identity
- Linear Spaces
- Linear Independence
- Spanning Sets and Independent Sets
- Exam I -Practise Questions
- Euclidean Space
- Lines in Euclidean Space
- Gram Schmidt Algorithm
- Orientation in $R^2$
- The Vector Product
- Planes
- Linear Equations
- Linear Equations – Simple Examples
- Subspaces (updated April 27 2019)
- The Hermite Normal Form
- Matrix of a Linear Map
- Dimensions of Kernel and Image
- The Null Space of a Matrix
- Finding the Left Nullspace
- Determinants.
- Determinant of a Direct Product.
- Graph Matrices
- Circuits
- Closure
- Affine Spaces in Physics
- Distance to an Affine Subspace
- Convex Sets
- The Centroid
- Projection and Least Squares

#### Homework

### Texts

- Lang, Serge,
*Introduction to Linear Algebra*, Springer, 1997. - Gilbert Strang,
*Introduction to Linear Algebra*, Ed. 4, 2009.

### Bibliography

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