On the diagonal of the matrices in a similarity class
Abstract
Let A be an n by n matrix with entries in an arbitrary field, and c1,...,cn be scalars. We prove that if A is not a scalar multiple of the identity matrix, then the condition c1+...+cn=tr(A) is necessary and sufficient for A to be similar to a matrix with diagonal entries c1,...,cn.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.