Matrix multiplication II: Difference between revisions

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<html>
  <script type="text/javascript" src="/distrib/MathJax/MathJax.js"></script>
  <form>
  <input type="button" id="toggleButton" value="Show trace" onClick="toggleTrace()">
  </form>
</html>
<jsxgraph width="600" height="600">
<jsxgraph width="600" height="600">
  JXG.Options.text.useMathJax = true;
   var b1 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-10,10,10,-10], axis:true});
   var b1 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-10,10,10,-10], axis:true});
   b1.suspendUpdate();
   b1.suspendUpdate();
   var a = b1.create('slider',[[-5,-2],[5,-2],[-5,1,5]],{name:'a'});
   var a = b1.create('slider',[[-5,-2],[5,-2],[-5,1,5]],{name:'a', snapWidth:0.1});
   var b = b1.create('slider',[[-5,-3],[5,-3],[-5,0,5]],{name:'b'});
   var b = b1.create('slider',[[-5,-3],[5,-3],[-5,0,5]],{name:'b', snapWidth:0.1});
   var c = b1.create('slider',[[-5,-4],[5,-4],[-5,0,5]],{name:'c'});
   var c = b1.create('slider',[[-5,-4],[5,-4],[-5,0,5]],{name:'c', snapWidth:0.1});
   var d = b1.create('slider',[[-5,-5],[5,-5],[-5,1,5]],{name:'d'});
   var d = b1.create('slider',[[-5,-5],[5,-5],[-5,1,5]],{name:'d', snapWidth:0.1});


   var v = b1.create('point',[2,2],{style:5,name:'v'});
   var v = b1.create('point',[2,2],{face:'o', size:2, name:'v'});
  var w = b1.create('point',[-2,1],{style:5,name:'w'});
   var va = b1.create('arrow',[[0,0],v]);
   var va = b1.create('line',[[0,0],v],{straightFirst:false, straightLast:false, lastArrow:true});
  var wa = b1.create('line',[[0,0],w],{straightFirst:false, straightLast:false, lastArrow:true});


  var b2 = JXG.JSXGraph.initBoard('box2', {originX: 150, originY: 150, unitX: 20, unitY: 20});
   var v2 = b1.create('point',[
   var v2 = b1.create('point',[
       function() {return a.Value()*v.X()+b.Value()*v.Y();},
       function() {return a.Value()*v.X()+b.Value()*v.Y();},
       function() {return c.Value()*v.X()+d.Value()*v.Y();}],{style:7,name:"v'"});
       function() {return c.Value()*v.X()+d.Value()*v.Y();}],{face:'o', size:2, name:"v'", fillColor: 'black', strokeColor: 'black'});
   var w2 = b1.create('point',[
  var va2 = b1.create('arrow',[[0,0],v2],{strokeColor:'black', strokeWidth:1});
      function() {return a.Value()*w.X()+b.Value()*w.Y();},
 
      function() {return c.Value()*w.X()+d.Value()*w.Y();}],{style:7,name:"w'"});
   var t = b1.create('text',[-8, 5,
  var va2 = b1.create('line',[[0,0],v2],{straightFirst:false, straightLast:false, lastArrow:true});
            function(){ return '\\[ M = \\left(\\begin{matrix}'
  var wa2 = b1.create('line',[[0,0],w2],{straightFirst:false, straightLast:false, lastArrow:true});
                        + (a.Value()).toFixed(2) + '&'
   var t = b1.create('text',[-6,-2,function(){ return '|'+b1.round(a.Value(),2)+' '+b1.round(b.Value(),2)+'|'+'<br>'+'|'+b1.round(c.Value(),2)+' '+b1.round(d.Value(),2)+'|';}]);
                        + (b.Value()).toFixed(2) + '\\\\'
                        + (c.Value()).toFixed(2) +'&'
                        + (d.Value()).toFixed(2)+'\\end{matrix}\\right)\\]';}]);
 
   var t2 = b1.create('text',[-8,2,
              function(){ return "\\[\\lambda = \\frac{|v'|}{|v|} = "
                + (
                    JXG.Math.Geometry.distance([0,0],[v2.X(),v2.Y()])/
                    JXG.Math.Geometry.distance([0,0],[v.X(),v.Y()])
                  ).toFixed(3)  
                  + "\\]";}]);
   b1.unsuspendUpdate();
   b1.unsuspendUpdate();


showTrace = false;
var toggleTrace = function() {
  showTrace = !showTrace;
  v.setProperty({trace: showTrace});
  v2.setProperty({trace: showTrace});
  var b = document.getElementById("toggleButton");
  if (showTrace) {
    b.value = "Hide trace";
  } else {
    b.value = "Show trace";
    v.clearTrace();
    v2.clearTrace();
  }
};
</jsxgraph>
This example uses [http://mathjax.org MathJax].
=== The underlying JavaScript code ===
<source lang="javascript">
  JXG.Options.text.useMathJax = true;
  var b1 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-10,10,10,-10], axis:true});
  b1.suspendUpdate();
  var a = b1.create('slider',[[-5,-2],[5,-2],[-5,1,5]],{name:'a', snapWidth:0.1});
  var b = b1.create('slider',[[-5,-3],[5,-3],[-5,0,5]],{name:'b', snapWidth:0.1});
  var c = b1.create('slider',[[-5,-4],[5,-4],[-5,0,5]],{name:'c', snapWidth:0.1});
  var d = b1.create('slider',[[-5,-5],[5,-5],[-5,1,5]],{name:'d', snapWidth:0.1});
  var v = b1.create('point',[2,2],{face:'o', size:2, name:'v'});
  var va = b1.create('arrow',[[0,0],v]);
  var v2 = b1.create('point',[
      function() {return a.Value()*v.X()+b.Value()*v.Y();},
      function() {return c.Value()*v.X()+d.Value()*v.Y();}],{face:'o', size:2, name:"v'", fillColor: 'black', strokeColor: 'black'});
  var va2 = b1.create('arrow',[[0,0],v2],{strokeColor:'black', strokeWidth:1});
            function(){ return '\\[ M = \\left(\\begin{matrix}'
                        + (a.Value()).toFixed(2) + '&'
                        + (b.Value()).toFixed(2) + '\\\\'
                        + (c.Value()).toFixed(2) +'&'
                        + (d.Value()).toFixed(2)+'\\end{matrix}\\right)\\]';}]);
  var t2 = b1.create('text',[-8,2,
              function(){ return "\\[\\lambda = \\frac{|v'|}{|v|} = "
                + (
                    JXG.Math.Geometry.distance([0,0],[v2.X(),v2.Y()])/
                    JXG.Math.Geometry.distance([0,0],[v.X(),v.Y()])
                  ).toFixed(3)
                  + "\\]";}]);
  b1.unsuspendUpdate();


showTrace = false;
var toggleTrace = function() {
  showTrace = !showTrace;
  v.setProperty({trace: showTrace});
  v2.setProperty({trace: showTrace});
  var b = document.getElementById("toggleButton");
  if (showTrace) {
    b.value = "Hide trace";
  } else {
    b.value = "Show trace";
    v.clearTrace();
    v2.clearTrace();
  }
};
</source>


</jsxgraph>


[[Category:Examples]]
[[Category:Examples]]

Revision as of 15:27, 20 February 2013

This example uses MathJax.

The underlying JavaScript code

  JXG.Options.text.useMathJax = true;
  var b1 = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-10,10,10,-10], axis:true});
  b1.suspendUpdate();
  var a = b1.create('slider',[[-5,-2],[5,-2],[-5,1,5]],{name:'a', snapWidth:0.1});
  var b = b1.create('slider',[[-5,-3],[5,-3],[-5,0,5]],{name:'b', snapWidth:0.1});
  var c = b1.create('slider',[[-5,-4],[5,-4],[-5,0,5]],{name:'c', snapWidth:0.1});
  var d = b1.create('slider',[[-5,-5],[5,-5],[-5,1,5]],{name:'d', snapWidth:0.1});

  var v = b1.create('point',[2,2],{face:'o', size:2, name:'v'});
  var va = b1.create('arrow',[[0,0],v]);

  var v2 = b1.create('point',[
       function() {return a.Value()*v.X()+b.Value()*v.Y();},
       function() {return c.Value()*v.X()+d.Value()*v.Y();}],{face:'o', size:2, name:"v'", fillColor: 'black', strokeColor: 'black'});
  var va2 = b1.create('arrow',[[0,0],v2],{strokeColor:'black', strokeWidth:1});

            function(){ return '\\[ M = \\left(\\begin{matrix}' 
                        + (a.Value()).toFixed(2) + '&'
                        + (b.Value()).toFixed(2) + '\\\\'
                        + (c.Value()).toFixed(2) +'&' 
                        + (d.Value()).toFixed(2)+'\\end{matrix}\\right)\\]';}]);

  var t2 = b1.create('text',[-8,2,
               function(){ return "\\[\\lambda = \\frac{|v'|}{|v|} = " 
                 + (
                     JXG.Math.Geometry.distance([0,0],[v2.X(),v2.Y()])/
                     JXG.Math.Geometry.distance([0,0],[v.X(),v.Y()])
                   ).toFixed(3) 
                   + "\\]";}]);
  b1.unsuspendUpdate();

showTrace = false;
var toggleTrace = function() {
  showTrace = !showTrace;
  v.setProperty({trace: showTrace});
  v2.setProperty({trace: showTrace});
  var b = document.getElementById("toggleButton");
  if (showTrace) {
     b.value = "Hide trace";
  } else {
     b.value = "Show trace";
     v.clearTrace();
     v2.clearTrace();
  }
};