Projector associated with an eigenvector

Question

I am reading a research paper and I can't quite get what a projector associated with an eigenvector is.

extract from the research paper

where $\Lambda$ is an nxn matrix.

Can anyone please help. Many thanks.

Answer 1

Given an eigenvector there is an associated eigenspace (spanned by the vector). The corresponding projector is the orthogonal projection onto that subspace. If you take your eigenvector unitary say $u$ ) then the matrix of the projector is $P=uu^T$