Eigen Vectors

# Eigen Vectors - = → = AW1W2 W1W2λ100λ2...

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

Tuesday, November 03, 2009 Eigen Vectors ** = + x Ax bt = x0 x0 ** Eigenvalues/eigenvectors = Awi λiwi - Eigenvalues/Eige vectors of same or different values form linear independent sectors - Each Eigenvalue λ i has at least one Eigenvector - If m i is the multiplicity of λ i it is positive then λ i has 1, 2, 3… or m i eigenvectors Ex3. =- - → A 230 2 only one eigenvector Ex4. =- - A 200 2 2 eigenvector *If there are as many Eigenvectors as the size of the matrix, then there is a full set of the eigenvector nxn matrix A has n eigenvectors Assume a full set of eigenvectors: = AW1W2 Wn W1W2 Wn λ1000λ2000λn | | | | (eigenvector matrix)(eigenvalue matrix) In a 2x2 case

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = → = AW1W2 W1W2λ100λ2 a11a12a21a22w11w12w21w22 w11w12w21w22λ100λ2 → + + + + = a11w11 a12w21a11w12 a12w22a21w11 a22w21a21w12 a22w22 λ1w11λ2w12λ1w21λ2w22 = → … = … → = Aw1 λiwi AW1W2 Wn W1W2 Wnλ1000λ2000λn AW WΛ Multiply by W-1 if W is nxn matrix (full set of eigen vector)- = -→ = AWW 1 W 1WΛ A Λ 1 Tuesday, November 03, 2009 Back to ** in to top box Define = → = -( ) xt Wzt zt W 1x t = + → = + ; } = ddtWz AWz bt Wz AWz bt initial conditions change Wz0 x0 = = ddta ft adfdt ddtA ft Adfdt-= -+ -→ = + ( ) W 1Wz W 1AWz W 1bt z Λz ξ t | | | | Λ ξ 2...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Eigen Vectors - = → = AW1W2 W1W2λ100λ2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online