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Author Archives: Ofir
Minkowski’s theorem
In the post about Diophantine approximation, we saw that in order to find “good” rational approximations to a real number, it is enough to prove that given a lattice and a “big enough” box around the origin, the box must … Continue reading
From number theory to geometry of lattices
Number theory can mean a lot of thing to a lot of people. This is a very big part of mathematics, and it contains many areas starting with the elementary number theory (“simple” congruence like arguments), algebraic number theory (e.g. … Continue reading
From Diophantine approximation to geometry of numbers
We all know about Pythagoras and his obsession with triangles. Usually when we first learn about the rational and real numbers, we are also told about the Pythagoreans, a 6th century BCE cult that started with the followers of Pythagoras and … Continue reading
A wild lattice appears
A couple of years ago I began doing some research in a new mathematical area (at least new for me) and suddenly lattices began to appear everywhere. The thing that makes these lattices interesting is how they are connected to … Continue reading
The generic matrix and the Cayley–Hamilton theorem
Sometime during the first course in linear algebra we all learn the famous Cayley-Hamilton theorem which states the following: Theorem: Let be an matrix over a field , and denote by its characteristic polynomial. Then . The “easy” proof for … Continue reading
Ofir David 