<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@4e453dfa5b934266859d53be74a8c5f1" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<h2 class="hd hd-2 unit-title">3.4 Session Overview</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@e1a7e907012d4f819c19a2ba8571d0bd">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@e1a7e907012d4f819c19a2ba8571d0bd" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<div style="float: left; margin: 6px 20px auto 0px;"><img height="100" width="100" src="/assets/courseware/v1/09a720781ce03b849d42f706a779b8eb/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_4_Session_Overview.jpg" alt="Figured excerpted from 'Introduction to Linear Algebra' by G.S. Strang" /></div>
<p></p>
<p>After a final discussion of positive definite matrices, we learn about "similar" matrices: <em>B = M<sup>−1</sup>AM</em> for some invertible matrix <em>M</em>. Square matrices can be grouped by similarity, and each group has a "nicest" representative in <em>Jordan normal form.</em> This form tells at a glance the eigenvalues and the number of eigenvectors.</p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@b37ae8f85e7e4f69859c4f7f3a0c76cd" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<h2 class="hd hd-2 unit-title">Lecture Video</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@video+block@762b4cda9e754427815ba1a5ef610a61">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="video" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@video+block@762b4cda9e754427815ba1a5ef610a61" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Similar Matrices and Jordan Form</h3>
<div
id="video_762b4cda9e754427815ba1a5ef610a61"
class="video closed"
data-metadata='{"autoplay": false, "speed": null, "duration": 0.0, "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "ytTestTimeout": 1500, "showCaptions": "true", "savedVideoPosition": 0.0, "completionEnabled": false, "ytMetadataEndpoint": "", "sources": ["https://archive.org/download/MIT18.06S05_MP4/28.mp4"], "autohideHtml5": false, "autoAdvance": false, "transcriptAvailableTranslationsUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@762b4cda9e754427815ba1a5ef610a61/handler/transcript/available_translations", "end": 0.0, "saveStateUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@762b4cda9e754427815ba1a5ef610a61/handler/xmodule_handler/save_user_state", "saveStateEnabled": false, "completionPercentage": 0.95, "ytApiUrl": "https://www.youtube.com/iframe_api", "captionDataDir": null, "transcriptLanguages": {"en": "English"}, "publishCompletionUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@762b4cda9e754427815ba1a5ef610a61/handler/publish_completion", "recordedYoutubeIsAvailable": true, "start": 0.0, "transcriptLanguage": "en", "transcriptTranslationUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@762b4cda9e754427815ba1a5ef610a61/handler/transcript/translation/__lang__", "prioritizeHls": false, "streams": "1.00:z_zYQHmrh08", "poster": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="762b4cda9e754427815ba1a5ef610a61"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_762b4cda9e754427815ba1a5ef610a61">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_762b4cda9e754427815ba1a5ef610a61">
<div class="wrapper-download-video">
<h4 class="hd hd-5">Video</h4>
<a class="btn-link video-sources video-download-button" href="https://archive.org/download/MIT18.06S05_MP4/28.mp4">
Download video file
</a>
</div>
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@762b4cda9e754427815ba1a5ef610a61/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@762b4cda9e754427815ba1a5ef610a61/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@0e1de6d4e01f4f629cbbeb549548bf9f">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@0e1de6d4e01f4f629cbbeb549548bf9f" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><a href="/assets/courseware/v1/bebe41675b1ffd773cbdec6e4488c143/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_4_Lectrans.pdf" target="[object Object]">Lecture video transcript (PDF)</a></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@ae3d29bc1dbf46cea467c67fa9c30b7f" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<h2 class="hd hd-2 unit-title">Lecture Summary and Reading</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@6b1cc916955a4e5886e9231ca40acbf7">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@6b1cc916955a4e5886e9231ca40acbf7" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<h3>Lecture Summary</h3>
<ul>
<li><a href="/assets/courseware/v1/1d4a43bc7ca20ae9e994144535fed4a0/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_4_Lecsum.pdf" target="[object Object]">Similar Matrices and Jordan Form (PDF)</a></li>
</ul>
<h3>Suggested Reading</h3>
<ul>
<li>Read Section 6.6 in the 4<sup>th</sup> edition or Section 6.2 in the 5<sup>th</sup> edition.</li>
</ul>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@ecb86f9d8e1148fd909d371c9d356bcb" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<h2 class="hd hd-2 unit-title">Recitation Video</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@video+block@a329079ad4af4178b463b38b49d829aa">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="video" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@video+block@a329079ad4af4178b463b38b49d829aa" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Similar Matrices</h3>
<div
id="video_a329079ad4af4178b463b38b49d829aa"
class="video closed"
data-metadata='{"autoplay": false, "speed": null, "duration": 0.0, "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "ytTestTimeout": 1500, "showCaptions": "true", "savedVideoPosition": 0.0, "completionEnabled": false, "ytMetadataEndpoint": "", "sources": ["https://archive.org/download/MIT18.06SCF11/MIT18_06SC_110607_B1_300k.mp4"], "autohideHtml5": false, "autoAdvance": false, "transcriptAvailableTranslationsUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@a329079ad4af4178b463b38b49d829aa/handler/transcript/available_translations", "end": 0.0, "saveStateUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@a329079ad4af4178b463b38b49d829aa/handler/xmodule_handler/save_user_state", "saveStateEnabled": false, "completionPercentage": 0.95, "ytApiUrl": "https://www.youtube.com/iframe_api", "captionDataDir": null, "transcriptLanguages": {"en": "English"}, "publishCompletionUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@a329079ad4af4178b463b38b49d829aa/handler/publish_completion", "recordedYoutubeIsAvailable": true, "start": 0.0, "transcriptLanguage": "en", "transcriptTranslationUrl": "/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@a329079ad4af4178b463b38b49d829aa/handler/transcript/translation/__lang__", "prioritizeHls": false, "streams": "1.00:KUuxdk_V7To", "poster": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="a329079ad4af4178b463b38b49d829aa"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_a329079ad4af4178b463b38b49d829aa">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_a329079ad4af4178b463b38b49d829aa">
<div class="wrapper-download-video">
<h4 class="hd hd-5">Video</h4>
<a class="btn-link video-sources video-download-button" href="https://archive.org/download/MIT18.06SCF11/MIT18_06SC_110607_B1_300k.mp4">
Download video file
</a>
</div>
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@a329079ad4af4178b463b38b49d829aa/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:OCW+18.06SC+2T2019/xblock/block-v1:OCW+18.06SC+2T2019+type@video+block@a329079ad4af4178b463b38b49d829aa/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@312c3a4b1d0c414abb595ddcb504a9c4">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@312c3a4b1d0c414abb595ddcb504a9c4" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p><a href="/assets/courseware/v1/dfaab4ce95491d76733e4de6f0ad235d/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_4_Rectrans.pdf" target="[object Object]">Recitation video transcript (PDF)</a></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="vertical" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@vertical+block@e3d8951872b54c8692ed5f49f2aa718f" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<h2 class="hd hd-2 unit-title">Problems and Solutions</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:OCW+18.06SC+2T2019+type@html+block@3a4225ac270c43c58fd14f34445545c3">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-runtime-version="1" data-course-id="course-v1:OCW+18.06SC+2T2019" data-graded="False" data-block-type="html" data-has-score="False" data-usage-id="block-v1:OCW+18.06SC+2T2019+type@html+block@3a4225ac270c43c58fd14f34445545c3" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-request-token="c3b5acbc37f311f0ad0b0e09798aea1b">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p>Work the problems on your own and check your answers when you're done.</p>
<p><a href="/assets/courseware/v1/d399865e39920cb62b7ea554223b111e/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_4_Exercises.pdf" target="[object Object]">Exercises on similar matrices and Jordan Form (PDF)</a></p>
<p><a href="/assets/courseware/v1/789956d68d1adb808538dac68d6f40e6/asset-v1:OCW+18.06SC+2T2019+type@asset+block/18.06_Unit_III_3_4_Solutions.pdf" target="[object Object]">Solutions to similar matrices and Jordan Form (PDF)</a></p>
</div>
</div>
</div>
</div>