5.2 - MATH1850U/2050U Chapter 5 cont 1 EIGENVALUES AND...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH1850U/2050U: Chapter 5 cont… 1 EIGENVALUES AND EIGENVECTORS cont… Diagonalization (Section 5.2; pg. 305) Two Equivalent Problems we consider: 1. The Eigenvector Problem: Given an n n matrix A , does there exist a basis for n R consisting of eigenvectors of A ? 2. The Diagonalization Problem (Matrix Form): Given an n n matrix A , does there exist an invertible matrix P such that AP P 1 is a diagonal matrix? Definition: A square matrix A is called diagonalizable if there is an invertible matrix P such that AP P 1 is a diagonal matrix; the matrix P is said to diagonalize A . Example: Consider A and P below. Show that A is diagonalizable.
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
MATH1850U/2050U: Chapter 5 cont… 2 Theorem: If A is an n n matrix, then the following are equivalent: a) A is diagonalizable. b) A has n linearly independent eigenvectors. Remark: Since A is n n , the eigenvectors are in R n . Thus, b) implies that the eigenvectors form a basis for R n . Example:
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 4

5.2 - MATH1850U/2050U Chapter 5 cont 1 EIGENVALUES AND...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online