MATH 6112 Advanced Linear Algebra

Fall 2017

MW 4:30-5:45

Professor Federico Bonetto

Office Hours: MW 5:45-7:00, classroom;

The argument covered will include:

• Review of Vector Spaces, Matrices and Canonical Form.
• Schur decomposition, SVD, and their consequences.
• Positive (Nonnegative) Matrices: Perron Frobenius Theory
• Matrices depending on parameters

I'll use the notes by prof. Dieci. The note will be distributed during class hours.

The syllabus can be found here.

There will be two midterms. The first midterm will be in class and will take place on Monday October 2nd. The second midterm will a take home exam on the first week of november.

The final grade will be based on the following rules: 40% final, 60% midterms. Curving will be done on the final result.

First week

Material covered:

• (1.2) Field
• (1.3) Vector Space
• (1.4) Eigenvalues and Eigenvectors

Second week

Material covered:

• (1.5) Matrices and canonical forms

Third and Fourth week

Material covered:

• (2.1) Inner Product
• (2.2) Other norms.
• (2.3) Self-adjoint (symmetric) and normal matrices.

Fifth, sixth, and seventh week

Material covered:

• (2.3.1) Projections and Eigenspaces
• (3.2.2) Positive definiteness and congruence

First Midterm will be on Monday September 23. Here is the solution set.

Material covered:

• (3.2.3) More inner products and projections
• (4) Matrices with Nonnegative Entries: Perron Frobenius Theory.