![arXiv:math/0607084v3 [math.NT] 26 Sep 2008](http://s1.studyres.com/store/data/014838781_1-63e86760b3063903e159a8155f16fef1-300x300.png)
1: Introduction to Lattices
... An immediate consequence of Theorem 4 is that for any matrix B with full column rank, the set L(B) is a lattice according to de nition De nition Notice that the lower bound mini kb∗i k depends on the choice of the basis. We will see later in the course that some bases give better lower bounds than o ...
... An immediate consequence of Theorem 4 is that for any matrix B with full column rank, the set L(B) is a lattice according to de nition De nition Notice that the lower bound mini kb∗i k depends on the choice of the basis. We will see later in the course that some bases give better lower bounds than o ...
hyperbolic pairs and basis
... Then b(u, u) = 1, b(v, v) = −1, and b(u, v) = b(v, u) = 0. Alternatively we find under this basis we have the quadratic form q(xu + yv) = x2 − y 2 which is also seen as the standard equation of a hyperbola. If we think of a quadratic form as generalizing norms – that is length, then we are observing ...
... Then b(u, u) = 1, b(v, v) = −1, and b(u, v) = b(v, u) = 0. Alternatively we find under this basis we have the quadratic form q(xu + yv) = x2 − y 2 which is also seen as the standard equation of a hyperbola. If we think of a quadratic form as generalizing norms – that is length, then we are observing ...
