J. B. Nation

J. B. Nation
Department of Mathematics
University of Hawaii
Honolulu, HI 96822
Telephone: 808-956-4655
Fax: 808-956-9139
E-mail: jb@math.hawaii.edu

Publications

Syllabus
Linear Algebra review
Homework 1: Exercises 1.1, 1.3, 1.4, 1.7-1.10, 1.13, 1.15, 1.16
Homework 2: Exercises 1.22, 1.23, and the following problem from Householder. Define the elementary matrix $E(u,v,sigma) = I-sigma.u.v^T. Find E(u,v,sigma).E(u,v,tau), and use this formula to find (E(u,v,sigma))^{-1}. Give an example.
Quiz due Groundhog Day: Analyze an example of a system Ax=b for specific matrices A that are (1) 5x3, (2) 3x3, (3) 4x2.
Homework 3: Exercises 3.4, 3.15 and the following problem. Let A be an invertible square matrix, and let M be a matrix of the block form [A B]. Show that for any appropriately sized matrix C, the matrix M has a right inverse of the form [X C]^T. Give an example. Explain how to use the same technique to obtain left inverses.