Math 726  University of South Carolina
D. Meade  Spring 1996

Assignment #1: Introduction to Matrix Computations

Due: Friday, 19 January 1996

\underline{Reading assignment}:

Text Section Comments

G/VL 1.1, 1.2 pay particular attention to the saxpy and gaxpy operations and the variety of algorithms available for the different matrix multiplications

C  1.1  compare the notation and terminology between G/VL and C

\underline{Problems from Golub and VanLoan}:

Section Page Problems
1.1  15 # 1.1.3 (attempt to minimize the number of multiplications)

# 1.1.4

1.2  25 # 1.2.5
2.2  52 # 2.1.2, 2.1.3, 2.1.4

Other Problems

• Verify formula (2.1.4), p. 51, of G/VL.

• Show that if v_{1}, v_{2}, …, v_{k} ∈ R^{n} are orthonormal, then they are linearly independent.

\underline{Notes}

• These problems have been selected to lay a common foundation from which we can add new knowledge. Some of the necessary information will not be covered in class. The reading assignments have been selected to supplement the necessary information.

• You are encouraged to work together with your classmates. However, any solution you turn in must be prepared by you – no copying of solutions.

• If you have any questions, please ask in class, in office hours, by e-mail, . . ..