1. Assume that the operation A. ∗ B, where A and B are
matrices multiplies corresponding entries to form a new matrix. For instance,
Write an algorithm to form A. ∗ B.
2. Definition 6.4 within the problems of Chapter 6 defines the cross product of two vectors. Develop pseudocode for a function crossprod that computes the cross product of vectors
and
3. Write an efficient algorithm, addsym, that forms the sum of two
symmetric matrices.
4. Section 9.4 defined a tridiagonal matrix. Develop an algorithm trimul that forms the product of two
tridiagonal matrices.
5. An upper bidiagonal matrix is a matrix with a main diagonal and one upper diagonal:
Develop an algorithm, bisolve, to solve a system of equations
that uses only the nonzero elements.
6. Develop an algorithm lowtrimul that forms the product of two lower triangular matrices.
7. Show that the flop count for Algorithm 9.5 is
2
8. Compute the product of the two block matrices.