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<h2 class="hd hd-2 unit-title">Least Squares, Determinants and Eigenvalues</h2>
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<p><img height="240" width="350" src="/assets/courseware/v1/a75c4d8c25abeafebeb31b052d577a22/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_II_Overview.jpg" alt="Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang" /></p>
<p class="caption"><span style="color: #999999;">A graph and its edge-node incidence matrix.</span></p>
<p>Each component of a vector in <span style="color: #333333; font-family: arial, helvetica, sans-serif; font-size: 12px;">R</span><sup style="margin: 0px; padding: 0px; border: 0px; color: #333333; font-family: arial, helvetica, sans-serif;">n</sup> indicates a distance along one of the coordinate axes. This practice of dissecting a vector into directional components is an important one. In particular, it leads to the "least squares" method of fitting curves to collections of data. This unit also introduces matrix <em>eigenvalues</em> and <em>eigenvectors.</em> Many calculations become simpler when working with a basis of eigenvectors.</p>
<p>The <em>determinant</em> of a matrix is a number characterizing that matrix. This value is useful for determining whether a matrix is singular, computing its inverse, and more.</p>
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