Chapter6 - Chapter 6: Eigensystems Keith E. Emmert...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 6: Eigensystems Keith E. Emmert Eigenvalues and Eigenvectors Chapter 6: Eigensystems Keith E. Emmert Tarleton State University January 15, 2010 Chapter 6: Eigensystems Keith E. Emmert Eigenvalues and Eigenvectors Overview Eigenvalues and Eigenvectors Chapter 6: Eigensystems Keith E. Emmert Eigenvalues and Eigenvectors Definition Definition 1 Let A be any matrix, real or complex. A number is an eigenvalue of A if the equation Ax = x is true for some a58a58a58a58a58a58a58a58 nonzero a58a58a58a58a58a58a58 vector x . The vector x is an eigenvector associated with the eigenvalue . Remark 2 Eigenvalues and eigenvectors may be complex. Definition 3 Let L be a linear operator mapping a vector space V into itself. If L v = v and v negationslash = , then we call an eigenvalue and v an eigenvector of L . Chapter 6: Eigensystems Keith E. Emmert Eigenvalues and Eigenvectors A Word about Complex Eigenvalues Theorem 4 If A is a real matrix and has a complex eigenvalue , then the conjugate, , is also an eigenvalue and Ax = x and A x = x . Chapter 6: Eigensystems Keith E. Emmert Eigenvalues and Eigenvectors Theory and the Characteristic Equation Theorem 5 A scalar is an eigenvalue of a matrix A if and only if Det (...
View Full Document

This note was uploaded on 01/16/2012 for the course MATH 332 taught by Professor Keithemmert during the Spring '11 term at Tarleton.

Page1 / 16

Chapter6 - Chapter 6: Eigensystems Keith E. Emmert...

This preview shows document pages 1 - 6. Sign up to view the full document.

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