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<p>If <em>A</em> has <em>n</em> independent eigenvectors, we can write <em>A</em> = <em>SΛS</em><sup>−1,</sup> where Λ is a diagonal matrix containing the eigenvalues of<em> A</em>. This allows us to easily compute powers of <em>A</em> which in turn allows us to solve difference equations u<sub>k+1</sub> = <em>A</em>u<sub>k</sub>.</p>
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<p><a href="/assets/courseware/v1/0dc218d03fddeadfe5759d52e9eabc91/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_2.9_LecTrans.pdf" target="[object Object]">Lecture video transcript (PDF)</a></p>
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<h3>Lecture Summary</h3>
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<h3>Suggested Reading </h3>
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<li>Read Section 6.2 in the 4<sup>th</sup> or 5<sup>th</sup> edition.</li>
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<p>Work the problems on your own and check your answers when you're done.</p>
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