Eigen Vectors - = = AW1W2 W1W21002 a11a12a21a22w11w12w21w22...

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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
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Unformatted text preview: = = AW1W2 W1W21002 a11a12a21a22w11w12w21w22 w11w12w21w221002 + + + + = a11w11 a12w21a11w12 a12w22a21w11 a22w21a21w12 a22w22 1w112w121w212w22 = = = Aw1 iwi AW1W2 Wn W1W2 Wn10002000n AW W Multiply by W-1 if W is nxn matrix (full set of eigen vector)- = - = AWW 1 W 1W A 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 z t | | | | 2...
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Eigen Vectors - = = AW1W2 W1W21002 a11a12a21a22w11w12w21w22...

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