Unitary group

Imagine you have a big group of friends who all want to dance together. They all have their own dance moves and they want to make sure that they can all dance together in harmony. They decide to form a unitary group.

A unitary group is like a group of dancers who need to coordinate their moves so that they all work together. Just like how dancers have to follow a certain rhythm and tempo, members of a unitary group have to follow certain mathematical rules. These rules ensure that their actions don't clash with each other and that they work together in a seamless manner.

In mathematics, a unitary group is a type of group that consists of elements that preserve certain structures, such as the length and angle of a vector. Just like how dancers need to follow a certain rhythm and tempo, members of a unitary group have to follow certain mathematical rules to preserve these structures.

For example, imagine that you have a spinning top that is rotating at a certain speed. If you apply a unitary transformation to that top, it will still be spinning at the same speed and in the same direction. The transformation doesn't change the length or angle of the vector that represents the spinning top.

In summary, a unitary group is like a group of dancers who need to coordinate their moves to work together in harmony. For a unitary group, members have to follow certain mathematical rules to preserve certain structures, such as the length and angle of a vector.