Lineaariryhmät
Lineaariryhmät, also known as linear groups, are a fundamental concept in group theory, a branch of abstract algebra. They are groups whose underlying set is a vector space over a field, and whose group operation is compatible with the vector space structure. This compatibility is expressed through the condition that the group operation is a linear map with respect to the vector space operations.
Linear groups can be classified based on their underlying vector space and the field over which it
The study of linear groups involves examining their subgroups, homomorphisms, and automorphisms. For instance, the orthogonal
Linear groups have numerous applications in physics and engineering. For example, they are used to describe