# Search results

1. ### Here's an extension of a list posted earlier. If anybody can think of

Here's an extension of a list posted earlier. If anybody can think of any additions to the list, please post :D! Perspectives of the world: ------------------------------- Optimist – The glass is half-full. Pessimist – The glass is half-empty. Existentialist – The glass is. Fatalist – The...
2. ### A is similar to B is equivalent to A^k is similar to B^k?

Homework Statement Given two matrices, A and B. Is the following statement true? A is similar to B \Longleftrightarrow A^k is similar to B^k. Homework Equations By definition, A and B are similar if there exists an invertible matrix P such that B = P-1AP. The Attempt at a...
3. ### How to prove that rank is a similarity invariant?

1. Prove that the rank of a matrix is invariant under similarity. Notes so far: Let A, B, P be nxn matrices, and let A and B be similar. That is, there exists an invertible matrix P such that B = P-1AP. I know the following relations so far: rank(P)=rank(P-1)=n ; rank(A) = rank(AT); rank(A) +...