One semester course on linear algebra. Assuming a basic acquaintance with vectors and matrices, the course goes on to study matrix theory in greater depth as well as some of its applications. Topics include Gauss elimination, LU factorization, row, column and null spaces and their dimensions, orthogonality, Gram-Schmidt method, QR factorization, determinants, eigenvalues, symmetric and Hermitian matrices and linear transformations. Applications include Markov chains, linear difference equations, method of least squares, principle axes for conic sections, etc.

Two books will be used, both of which are available as free downloads and also as inexpensive paperbacks. Some topics are covered better in one book than in the other and the style is a bit different so it will be useful to use both this semester.

The first book is:

Linear Algebra, by Kwak and Hong. The book is available as a free download for UM student from the following URL: Kwak and Hong Book (http://z.umn.edu/LinearAlgebraKwak). At this webpage you can also order a softcover copy of the book at a reasonable price.The other book is:

Applied Linear Algebra and Matrix Analysis, by Thomas Shores. This book is also available as a free download and inexpensive purchase at: Shores Book (http://z.umn.edu/LinearAlgebraShores).

There will be grades for quizzes and three midterm exams. All exams and quizzes are open book/notes, calculators allowed.

Quizzes 25 % Midterm Exams (25% each) 75 % For general policy statements about grades and academic honesty, see: Academic Policies.

Midterm I | Monday, October 6 |

Midterm II | Monday, November 10 |

Midterm III | Monday, December 15 (final exam day but it is MT III) |

Homework will be assigned but not collected. Instead there will be weekly quizzes consisting of problems very similar to the homework problems. If you can do the homework problems you should have no trouble with the quizzes. One quiz score will be dropped to allow for an absence or just a "bad day." To see the assignments, click on the link above.

Here is a tentative week by week outline of the course. For the readings (K means Kwak and Hong, S means Shores).

Week |
Topic |
Reading |

9/3 | Linear eqs., matrix ops, applications | K Ch.1, S 1.1-1.4 |

9/8-9/10 | Rref, rank, nullity, inverses, LU, LDU | K Ch. 1, S 2.1-2.5 |

9/15-9/17 | Determinants, applications | K Ch 2, S 2.6 4 |

9/22-9/24 | Vector spaces, subspaces, bases, dimension | K 3.1-3.4,S 3.1-3.3,3.5 |

9/29-10/1 | Matrix subspaces, lin. eqs. revisited | K 3.5-3.7, S 3.4,3.6 |

10/6-10/8 | Midterm I, Linear maps | K 4.1-4.3 |

10/13-10/15 | Change of basis, similarity, applications | K 4.5-4.7 |

10/20-10/22 | Eigenvalues, diagonalization | K 6.1-6.2, S 5.1-5.2 |

10/27-10/29 | Applications: Discrete DS, Markov chains | K 6.3, S 5.3 |

11/3-11/5 | Inner products, orthogonality | K 5.1-5.3,S 4.1,6.1-6.2 |

11/10-11/12 | Midterm II, Orthogonal bases, Gram-Schmidt | K 5.4, S 6.3 |

11/17-11/19 | Orthog. projection, isometries | K 5.5-5.8, S 6.4 |

11/24-11/26 | Least squares, QR, Thanksgiving | K 5.9, S 4.2,4.3, 6.4 |

12/1-12/3 | Quadratic forms, orthogonal diagonalization | K 9.1-9.4, S 5.4 |

12/8-/12/10 | Singular values, applications | S 5.5-5.6 |

12/15 | Midterm III |