Eigen Vectors - = → = AW1W2 W1W2λ100λ2...

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

View Full Document Right Arrow Icon
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
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
Background image of page 2
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 Right Arrow Icon
Ask a homework question - tutors are online