# MATH 310: Applied Linear Algebra

### COURSE DESCRIPTION

Matrices, Gaussian elimination, vector spaces, LU-decomposition, orthogonality, Gram-Schmidt process, determinants, inner products, eigenvalue problems, applications to differential equations and Markov processes. Credit is not given in both Mathematics 310 and 320.

### TEXTBOOK

Steven J. Leon, Linear Algebra with Applications (8th edition), Prentice-Hall, 2009.

### SCHEDULE

This is a suggested course schedule. Individual sections may vary somewhat in their precise content and schedules.

 CHAPTER 1: LINEAR EQUATIONS Week 1. § 1.1 Linear Systems & Row Operations § 1.2 Gauss-Jordan Operation on Matrices Week 2. § 1.3 Matrix Arithmetic § 1.4 Matrix Algebra Week 3. § 1.5 Elementary matrices; LU-decomposition CHAPTER 2: DETERMINANTS Week 4. § 2.1 Computation by elimination and/or cofactors § 2.2 Properties § 2.3 Cramer's rule CHAPTER 3: VECTOR SPACES Week 5. § 3.1 Examples § 3.2 Subspaces (how to verify), span Week 6. § 3.3 Linear independence § 3.4 Basis and dimension Week 7. § 3.5 Change of basis (coordinates, transition matrix) § 3.6 Row space & column space CHAPTER 4: LINEAR TRANSFORMATIONS Week 8. § 4.1 Linear transformations - definition & examples § 4.2 Matrix representation § 4.3 Similarity, look ahead to diagonalization in § 6.3 CHAPTER 5: ORTHOGONALITY Week 9. § 5.1 Dot product § 5.2 Orthogonal subspaces Week 10. § 5.3 Least squares, pseudo-inverses § 5.4 General inner product spaces, Cauchy-Schwarz inequality Week 11. § 5.5 Orthonormal basis and projection § 5.6 Gram-Schmidt process and QR-factorization CHAPTER 6: EIGENVALUES Week 12. § 6.1 Definition: Eigenvalues and eigenvectors; example: Markov Matrices § 6.2 Linear differential systems Week 13. § 6.3 Diagonalization, matrix exponential; "defective" (or non-diagonalizable) matrices § 6.4 Hermitian matrices: including symmetric matrices Week 14. § 6.6 General quadratic forms ( as time permits) § 6.7 Positive definite matrices (as time permits) Week 15. § 6.8 Nonnegative matrices (as time permits)

### STUDENTS WITH DISABILITIES

Students with disabilities who require special accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS). Students who need exam accommodations must contact ODS in the first week of the term to arrange a meeting with a Disability Specialist.