Applied Mathematics 1411A/B Chapter 5: Chapter 5 List of Theorems

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

Document Summary

If a is an n x n matrix, then a nonzero vector x in rn is called an eigenvector of a (or of the matrix operator ta) if ax is a scalar multiple of x; that is. The scalar is called an eigenvalue of a (or of ta), and x is said to be an eigenvector of a corresponding to . 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. Well, we know now that looking at any n x n matrix a, it will have the same number of eigenvalues as it has rows of columns. If a is an n x n triangular matrix (upper triangular, lower triangular, or diagnol), then the eigenvalues of a are the entries on the main diagnol of a.