O'Reilly logo

Algebra I: A Basic Course in Abstract Algebra by Rajendra Kumar Sharma, Sudesh Kumari Shah, Asha Gauri Shankar

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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 images be a linear transformation. ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required