I'm studying for a linear algebra final, and I'm looking over an old final our prof gave us and I've come across something I don't remember ever hearing anything about... Here's the problem: Write down a matrix A for the following condition: A is a 3x3 matrix with lambda=4 with algebraic multiplicity 3 and with geometric multiplicity 1. ...I don't have a problem with eigenvalues or anything, but I don't believe he ever mentioned algebraic multiplicity or geometric multiplicity. Is this another concept in linear algebra?? Or is this something way simple that I'm looking way too far into. ...What does he mean by algebraic multiplicity and geometric multiplicity?? Thanks!