## MTH 2775: Linear Algebra

#### Description

Study of general vector spaces, linear systems of equations, linear transformations and compositions, Eigenvalues, eigenvectors, diagonalization, modeling and orthogonality. Provides a transition to formal mathematics.
#### Textbook

Lecture Notes in Linear Algebra, T. Shaska (will be provided in class for free)
Linear algebra with applications, Otto Bretscher
#### Course policies

For all the problems and concerns you might have you must talk to me. No makeups will
be given other then in case of documented emergencies. The use of cellular phones or any other electronic equipment is NOT allowed during lectures. No calculators of any kind are allowed.
Further, I do not tolerate any kind of academic dishonesty. Appropriate measures according to Oakland University regulations will be taken for any case of cheating or breaking other rules. Attendance is mandatory!
#### Detailed Syllabus

A copy of the current semester of the detailed syllabus can be found here.
#### Contents

The following list of topics will be followed very closely.
Lecture 1: A word on analytic geometry
Lecture 2: Vectors in Physics and geometry
Lecture 3: Euclidean spaces and linear systems
Lecture 4: Row operations, algebra of matrices
Lecture 5: Introduction to vector spaces, bases and dimension
Lecture 6: Subspaces associated to a matrix, nullity and rank
Lecture 7: Sums, direct sums, direct products
Lecture 8: Midterm I
Lecture 9: Linear maps
Lecture 10: Matrices associated to linear maps, change of basis
Lecture 11: Linear transformations in geometry
Lecture 12: Determinants, characteristic polynomial
Lecture 13: Eigenvalues, Eigenvectors, eigenspaces
Lecture 14: Complex eigenvalues
Lecture 15: Diagonalizing matrices
Lecture 16: Midterm II
Lecture 17: Inner products, orthogonal bases
Lecture 18: Orthogonal transformations and orthogonal matrices
Lecture 19: Least squares
Lecture 20: Sylvestre’s theorem
Lecture 21: Quadratic and binary forms
Lecture 22: Midterm III
Lecture 23: Symmetric matrices
Lecture 24: Positive definite matrices
Lecture 25: Singular values and singular value decomposition
Lecture 26: Review