Topics In Linear Algebra and Its Applications - STEM2
Topics In Linear Algebra and Its Applications - STEM2
Topics In Linear Algebra and Its Applications - STEM2
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with<strong>and</strong>A = m 2B = −2(k + k 2 )mC = (k + k 2 ) 2 − k 2 2 = k2 + 2kk 2 .Let a = (k + k 2 − λm) <strong>and</strong> b = −k 2 . Then since the determinant is 0, wemust havea 2 = b 2So eitherora = b,a = −b.The equations for the eigenvectors are<strong>and</strong>If a = b, then the eigenvector isaU 1 + bU 2 = 0,bU 1 + aU 2 = 0.[1−1]On the other h<strong>and</strong>, if a = −b, then the eigenvector is[11]The eigenvalues are λ 1 <strong>and</strong> λ 2 . Let a i be the value of a for eigenvalue λ i , <strong>and</strong>let b i be the value of b for eigenvalue λ i . Now let us compute with values assignedto the constants. Let m = 1, k = 1, <strong>and</strong> k 2 = 1/10. The computationis done with a Matlab script (Octave script). Call it coupled.m:33
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