In higher algebra, let a be an n-dimensional vector space, then what is the dimension of the vector space composed of all linear transformations on a?

In higher algebra, let a be an n-dimensional vector space, then what is the dimension of the vector space composed of all linear transformations on a?

The vector space composed of all linear transformations is isomorphic to the vector space composed of all matrices, so it is n ^ 2-dimensional

It is proved that the n-dimensional vector space can be written as the direct sum of N one-dimensional vector spaces

Let A1, A2,..., an be a set of bases of n-dimensional space V, then v = (direct sum) l (A1) + L (A2) +... + L (an), where l (AI) is the subspace generated by AI, l (AI) = {Kai} since A1, A2,..., an are the bases of V, any vector in V can be expressed linearly by A1, A2,..., an, so v = l (A1) + L (A2) +