<div class="xblock xblock-public_view xblock-public_view-vertical" data-has-score="False" data-runtime-class="LmsRuntime" data-request-token="e84fd7ac681211ef85f20214bd5530e3" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@bff8d162ee82435f980ca1be19a12d71" data-block-type="vertical" data-graded="False" data-init="VerticalStudentView" data-course-id="course-v1:OCW+18.06SC+2T2019" data-runtime-version="1">
<h2 class="hd hd-2 unit-title">Least Squares, Determinants and Eigenvalues</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@7c9103baae1c4565a2bea9d8dbd9a24f">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-has-score="False" data-runtime-class="LmsRuntime" data-request-token="e84fd7ac681211ef85f20214bd5530e3" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@7c9103baae1c4565a2bea9d8dbd9a24f" data-block-type="html" data-graded="False" data-init="XBlockToXModuleShim" data-course-id="course-v1:OCW+18.06SC+2T2019" data-runtime-version="1">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<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>
<p>Looking for something specific? The <a href="/courses/course-v1:OCW+18.06SC+2T2019/jump_to_id/51689f6d83d445f2b5ceea8924984b16" target="[object Object]">Resource Index</a> compiles links to most course resources in a single page. </p>
<p></p>
</div>
</div>
</div>
</div>