Please read Lectures 2, 3, and 4 in the textbook Numerical Linear Algebra by Trefethen and Bau. Then do the following exercises.
P8. On page 12 of the textbook, equation (2.4) says (AB) = B A . Prove this by showing that the matrix entries are equal.
P9. On page 21 of the textbook, equation (3.10) gives a formula for the 1-norm of an m n matrix. Prove it:
kAk1 = max kai k1:
1 i m
Exercise 2.6 in Lecture 2.
Exercise 3.2 in Lecture 3.
Exercise 3.3 in Lecture 3. Do parts (a) and (b) only.
Exercise 4.3 in Lecture 4. Use the svd command on A. Write a MATLAB/OCTAVE (or PYTHON, JULIA, . . . ) function of the form vismat(A). Start by checking that the input matrix A is in fact 2 2, and that its entries are real. Correctness of the program is more important than figure appearance.
