MATH 6112 Advanced Linear Algebra

Fall 2013

MW 3:00-4:30

Professor Federico Bonetto

Office Hours: MW 4:30-5:30, 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 syllabus can be found here.

There will be two midterm.

I will assign HW for collection collection every other week. The HW will be taken from the notes.

The final grade will be based on the following rules: 45% final, 35% midterms, 20% HW. Curving will be done on the final result.

First week

Material covered:

• (1.2) Field
• (1.3) Vector Space
• (1.4) Eigenvalues and Eigenvectors
• (1.5) Matrices and canonical forms

Second week

Material covered:

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

First HW due on Wednesday September 4.

Third week

Material covered:

• (2.3.1) Projections and Eigenspaces
• An application: 1d Ising model

First Midterm will be on Monday September 23. Check the notes for preparation material.

Fourth week

Material covered:

• (2.3.2) Positive definiteness and congruence.