This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Section 5.2 Diagonalization Definition: If A and B are square matrices, then we say that B is similar to A if there is an invertible matrix P such that B = P 1 AP. Facts: 1. A and B have the same determinant 2. A is invertible if and only if B is invertible 3. A and B have the same rank 4. A and B have the same nullity 5. A and B have the same trace 6. A and B have the same charactesitic polynomial 7. A and B have the same eigenvalues 8. If λ is an eigenvalue of A and hence B, then the eigenspaces of A corresponding to λ and the eigenspace of B corresponding to λ have the same dimension Note: If B as described P 1 AP , is a diagonal matrix then finding eigenvalues and eigenspace of A will be much easier. Definition: A square matrix A is said to be diagonalizable if it is similar to some di agonal matrix; that is, if there exists an invertible matrix P such that P 1 AP is diagonal. In this case the matrix P is said to diagonalize A....
View
Full
Document
This document was uploaded on 04/26/2011.
 Spring '11

Click to edit the document details