Mike's lecture on vector spaces and dual spaces: Difference between revisions

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-: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-04-27 06:14:06 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-04-27 06:14:39 UTC</tt>.<br>
-: The original revision id was <tt>325945164</tt>.<br>
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 A monzo can also be viewed as a **VECTOR** in a **VECTOR SPACE**.
-For instance, the syntonic comma is |-4 4 -1&gt;. A geometric interpretation of this interval might be as a point in a space, like the point (-4, 4, -1). You'd plot this point by going -4 steps on the x axis, 4 steps on the y axis, and -1 steps on the z-axis. And if you really want to think of it like a vector in the sense that some high school or college algebra courses teach it, you can also draw an arrow with a big arrowhead from the origin that connects to this point. Here's a picture of that:
+For instance, the syntonic comma is |-4 4 -1&gt;. A geometric interpretation of this interval might be as a point in a space, like the point (-4, 4, -1). You'd plot this point by going -4 steps on the x axis, 4 steps on the y axis, and -1 steps on the z-axis. And if you really want to think of it like a vector in the sense that some high school or college algebra courses teach it, you can also draw an arrow with a big arrowhead from the origin that connects to this point. Here's a widget that lets you plot vectors:
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 A monzo can also be viewed as a &lt;strong&gt;VECTOR&lt;/strong&gt; in a &lt;strong&gt;VECTOR SPACE&lt;/strong&gt;.&lt;br /&gt;
 &lt;br /&gt;
-For instance, the syntonic comma is |-4 4 -1&amp;gt;. A geometric interpretation of this interval might be as a point in a space, like the point (-4, 4, -1). You'd plot this point by going -4 steps on the x axis, 4 steps on the y axis, and -1 steps on the z-axis. And if you really want to think of it like a vector in the sense that some high school or college algebra courses teach it, you can also draw an arrow with a big arrowhead from the origin that connects to this point. Here's a picture of that:&lt;br /&gt;
+For instance, the syntonic comma is |-4 4 -1&amp;gt;. A geometric interpretation of this interval might be as a point in a space, like the point (-4, 4, -1). You'd plot this point by going -4 steps on the x axis, 4 steps on the y axis, and -1 steps on the z-axis. And if you really want to think of it like a vector in the sense that some high school or college algebra courses teach it, you can also draw an arrow with a big arrowhead from the origin that connects to this point. Here's a widget that lets you plot vectors:&lt;br /&gt;
 &lt;br /&gt;
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