You can choose a base for and complete it to get a base of .
The main interest is to write in a simpler way.
Let V be a n-dimensional vector space, and let be a linear operator on
Suppose that is a -invariant subspace of ,
Show that there exists a basis for such that has the form
where is a matrix and is the zero matrix
The question itself confuses me. I am not sure what the question wants
If is a basis for , then has n vectors and
is a matrix
So what is this question asking us to reduce the matrix to a matrix with the entries themselves being matrices?