Lattice Basis Reduction

16 Lattice Basis Reduction

sides, find the components of the first side parallel and orthogona l to the

second side.

Exercise 1.2. Same as Exercise 1.1 for these p oints in R

2

:

A = (45, −81), B = (−50, −22), C = (−16, −9).

Exercise 1.3. Same as Exercise 1.1 for these p oints in R

3

:

A = (2, −9, 0), B = (−8, 2, −5), C = (−9, 7, 7).

Exercise 1.4. Same as Exercise 1.1 for these p oints in R

3

:

A = (77, 9, 31), B = (20, −61, −48), C = (24 , 65, 86).

Exercise 1.5. Same as Exercise 1.1 for these p oints in R

4

:

A = (4, −9, −2, −5), B = (1, 7, 8, −1), C = (−6, −8, −2, −2).

Exercise 1.6. Same as Exercise 1.1 for these p oints in R

4

:

A = (−62, −33, −68, −67), B = (42, 18, −59, 12), C = (52 , −13, 82, 72).

Exercise 1.7. Let C be an n×n matrix with integer entries and ...