Algebra I: A Basic Course in Abstract Algebra

Chapter 17

Eigenvectors and Eigenvalues

Let us consider a transformation of ℝ2, say projection on the x-axis. Under this transformation, every vector along x-axis remains invariant. Similarly under the reflection in the y-axis, every vector along the y-axis remains invariant. Under dilation every non-zero vector is stretched by a factor. Thus, a transformation may move some vectors parallel to themselves, that is, v → αv for some scalar α. Such vectors are called eigen vectors and are important for a transformation, and in this chapter we will learn to find them.

17.1 Eigenvectors and Eigenspace

Let T: ℝ² → ℝ² defined by T be a linear transformation. ...