Applied Mathematics 1411A/B Chapter 5.1.1: Applied Mathematics 1411A/B Chapter 5.1.: Applied Mathematics 1411A/B Chapter 5.1: Applied Mathematics 1411A/B Chapter 5.: Section 5.1.1

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

Document Summary

In this section we will define the notions of eigenvalue and eigenvector and discuss some of their basic properties. 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 . So, a vector is an eigenvector of a matrix if the product of that matrix and the vector is just a scalar multiple of that vector. That being that the vector is an eigenvalue of the matrix because the product of the matrix and the vector yields but a scalar multiple of the original thing. Compressing or stretching a vector as a normal scalar multiple would.