## 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*: ℝ^{2} → ℝ^{2} defined by *T* be a linear transformation. ...