We consider the following 4 square matrices of order 2 with coefficients in
Then we consider the following polynomials of degree 1 in
square matrices of order 2 for coefficients:
- How many additions and multiplications in
in order to compute the product
in a naive way.
- Check that Karatsuba's trick applies here (despite of the
fact that matrix multiplication is not commutative).
- Explain briefly why we can compute
using only 21 multiplications in
How many additions in
are needed in this case?
- Explain briefly in which circumstances using the
multiplication scheme of the previous question makes sense.
Marc Moreno Maza