Dividing Space According To A Lattice
A typical lattice Λ in thus has the form
where {v1, ..., vn} is a basis for . Different bases can generate the same lattice, but the absolute value of the determinant of the vectors vi is uniquely determined by Λ, and is denoted by d(Λ). If one thinks of a lattice as dividing the whole of into equal polyhedra (copies of an n-dimensional parallelepiped, known as the fundamental region of the lattice), then d(Λ) is equal to the n-dimensional volume of this polyhedron. This is why d(Λ) is sometimes called the covolume of the lattice.
Read more about this topic: Lattice Points
Famous quotes containing the words dividing and/or space:
“While you are divided from us by geographical lines, which are imaginary, and by a language which is not the same, you have not come to an alien people or land. In the realm of the heart, in the domain of the mind, there are no geographical lines dividing the nations.”
—Anna Howard Shaw (1847–1919)
“The flattering, if arbitrary, label, First Lady of the Theatre, takes its toll. The demands are great, not only in energy but eventually in dramatic focus. It is difficult, if not impossible, for a star to occupy an inch of space without bursting seams, cramping everyone else’s style and unbalancing a play. No matter how self-effacing a famous player may be, he makes an entrance as a casual neighbor and the audience interest shifts to the house next door.”
—Helen Hayes (1900–1993)