{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MAT211_Lecture18[1] - Consider the projection P on R2 onto...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MAT211 Lecture 18 Eigenvalues and eigenvectors Consider the projection P on R 2 onto the x-axis. Find all vectors v such that P(v) is parallel to v. Consider the reflection on R 2 with respect to the x-axis. Find all vectors v such that R(v) is parallel to v. Definition Consider an n x n matrix A. A vector v in Rn is an eigenvector if Av is a multiple of v, that is, if there exists a scalar k such that Av=kv. A scalar k such that Av=kv for some vector v is an eigenvalue . Example Consider an orthogonal projection onto a plane P on R 3 . Find all the eigenvalues and eigenvectors. Consider reflection with respect to a plane P on R 3 . Find all the eigenvalues and eigenvectors. Consider reflection with respect to a line L on R 3 . Find all the eigenvalues and eigenvectors. 5 Example • Consider the matrix of a rotation of angle ! /3 in R 2 . Find all the eigenvalues and eigenvectors. What are the eigenvalues and eigenvectors of any rotation?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}