JavaBinarySearchTree/matrices.html at main · soh2970/JavaBinarySearchTree · GitHub

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<html style="height: 100%;"><head>
<title>Matrices</title>

<body style="position: relative; min-height: 100%; top: 0px;">

	<h1 align="center"><font color="red">Matrices</font></h1>
	<p>A Matrix is an array of numbers.</p>

	<p>There are many things we can do with them ...</p>
	<h2>Adding</h2>
	<p>To add two matrices:  add the numbers in the matching positions:</p>
	<p align="center"><img src="matrix-addition.gif" alt="Matrix Addition" width="384" height="119"></p>
	<div class="simple">
	  <div align="center">These are the calculations:	    </div>
	  <table align="center">
          <tbody><tr align="center">
            <td>3+4=7</td>
            <td>8+0=8</td>
          </tr>
	    <tr align="center">
	      <td>4+1=5</td>
            <td>6-9=-3</td>
          </tr>
          </tbody></table>
	  </div>
	<p>The two matrices must be the same size, i.e. the rows must match in size, and the columns must match in size.</p>
	<div class="example">
	  <p>Example: a matrix with <b>3 rows</b> and <b>5 columns</b> can be added to another matrix of  <b>3 rows</b> and <b>5 columns</b>. But it could not  be added to a  matrix with <b>3 rows</b> and <b>4 columns</b> (the columns don't match in size)</p>
	  </div>
	<h2>Negative</h2>
	<p>The negative of a matrix is also simple:</p>
	<p align="center"><img src="matrix-negative.gif" alt="Matrix Negative" width="279" height="111"></p>
	<div class="simple">
      <div align="center">These are the calculations: </div>
	  <table align="center">
        <tbody><tr align="center">
          <td>-(2)=-2</td>
          <td>-(-4)=+4</td>
        </tr>
        <tr align="center">
          <td>-(7)=-7</td>
          <td>-(10)=-10</td>
        </tr>
      </tbody></table>
	  </div>
	<h2>Subtracting</h2>
	<p>To subtract two matrices: subtract the numbers in the matching positions:</p>
	<p align="center"><img src="matrix-subtraction.gif" alt="Matrix Subtraction" width="383" height="115"></p>
	<div class="simple">
      <div align="center">These are the calculations: </div>
	  <table align="center">
        <tbody><tr align="center">
          <td>3-4=-1</td>
          <td>8-0=8</td>
        </tr>
        <tr align="center">
          <td>4-1=3</td>
          <td>6-(-9)=15</td>
        </tr>
      </tbody></table>
	  </div>
      <p align="center"><i>Note: subtracting is actually defined as the <b>addition</b> of a negative matrix:  A + (-B)</i></p>
	<h2>Multiply by a Constant</h2>
	<p>We can multiply a matrix by some value:</p>
	<p align="center"><img src="matrix-multiply-constant.gif" alt="Matrix Multiply Constant" width="304" height="116"></p>
	<div class="simple">
      <div align="center">These are the calculations: </div>
	  <table align="center">
        <tbody><tr align="center">
          <td>2×4=8</td>
          <td>2×0=0</td>
        </tr>
        <tr align="center">
          <td>2×1=2</td>
          <td>2×-9=-18</td>
        </tr>
      </tbody></table>
	  </div>
	<p>We call the constant a <b>scalar</b>, so officially this is called <span class="large">"scalar multiplication"</span>. </p>