Applied Mathematics 1411A/B Chapter Notes - Chapter 5.1.2: Identity Matrix, Main Diagonal

• School: Western University
• Department: Applied Mathematics
• Course: Applied Mathematics 1411A/B
• Professor: Bogdan Tudose

Document Summary

Well lets start with some theorems to work our way there. Ax = ix where i is the identity matrix. This can be rearranged and factored to yield ( i - a)x = 0 which can eventually lead us to some interesting places. If a is an n x n matrix, then is an eigenvalue of a if and only if it satisfies the equation det( i - a) = 0. This is called the characteristic equation of a. Let"s use this concept to find the eigenvalues of. Recall that the identity matrix is a matrix of all ones and 0s where the main diagonal contains the ones. An vector is an eigenvector of a matrix a if the multiplication of that matrix a by the vector results in the vector being but a mere scalar multiple of the original.