<story><title>Matrix Multiplication</title><url>http://matrixmultiplication.xyz/</url></story><parent_chain><item><author>daniel-levin</author><text>This is a cool example of what Bret Victor calls an &amp;quot;Explorable Explanation&amp;quot; [0]. That said, I feel that it&amp;#x27;s more important to understand how and why matrix multiplication corresponds to a composition of linear transformations than learning the actual mechanics of doing the computation. You can get good at matrix multiplication without knowing what is going on. I view that as a less valuable activity than learning about linear transformations (vector-space structure preserving mappings) between finite dimensional vector spaces.&lt;p&gt;[0] &lt;a href=&quot;http:&amp;#x2F;&amp;#x2F;worrydream.com&amp;#x2F;ExplorableExplanations&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;worrydream.com&amp;#x2F;ExplorableExplanations&amp;#x2F;&lt;/a&gt;</text></item></parent_chain><comment><author>samuell</author><text>For understanding the mechanics of matrix multiplication, I found it useful to think in an analogy consisting of a grid of two layers of pipes; One -- the input-pipes -- coming in one direction, and the other -- the output pipes -- laid in an orthogonal direction. Then there would be &amp;quot;taps&amp;quot; in the cross-sections between the input and output pipes, representing the numbers (multiplication factors, really) in the matrix. I illustrated this in this little drawing: &lt;a href=&quot;http:&amp;#x2F;&amp;#x2F;imgur.com&amp;#x2F;gallery&amp;#x2F;gBs64&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;imgur.com&amp;#x2F;gallery&amp;#x2F;gBs64&lt;/a&gt;&lt;p&gt;The point then is that the taps (again, representing the matrix values) determine &lt;i&gt;how much of each item in the input vector, that should be mixed into each item in the output vector&lt;/i&gt;.&lt;p&gt;This analogy has the limitation that the taps are allowed to &lt;i&gt;enhance&lt;/i&gt; the flow, not just limit it, like physical taps would. That is, outputting more than 100% of the input :P Also, while this way of illustrating it may make some sense for matrix * vector multiplication, matrix * matrix would probably become a prohibitively cluttered image.</text></comment>
<story><title>Matrix Multiplication</title><url>http://matrixmultiplication.xyz/</url></story><parent_chain><item><author>daniel-levin</author><text>This is a cool example of what Bret Victor calls an &amp;quot;Explorable Explanation&amp;quot; [0]. That said, I feel that it&amp;#x27;s more important to understand how and why matrix multiplication corresponds to a composition of linear transformations than learning the actual mechanics of doing the computation. You can get good at matrix multiplication without knowing what is going on. I view that as a less valuable activity than learning about linear transformations (vector-space structure preserving mappings) between finite dimensional vector spaces.&lt;p&gt;[0] &lt;a href=&quot;http:&amp;#x2F;&amp;#x2F;worrydream.com&amp;#x2F;ExplorableExplanations&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;worrydream.com&amp;#x2F;ExplorableExplanations&amp;#x2F;&lt;/a&gt;</text></item></parent_chain><comment><author>ahane</author><text>3Blue1Brown is an amazing youtube channel that provides very entertaining and educating visual explanation for all sorts of maths.&lt;p&gt;He has a whole series on linear algebra, including matrix mulitplication:&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.youtube.com&amp;#x2F;playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.youtube.com&amp;#x2F;playlist?list=PLZHQObOWTQDPD3MizzM2x...&lt;/a&gt;</text></comment>