Matrix multiplication II: Difference between revisions

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<html>
  <input type="button" id="toggleButton" value="Show trace" onClick="toggleTrace()">
</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 va = b1.create('arrow',[[0,0],v]);
   var va = b1.create('arrow',[[0,0],v]);


   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 va2 = b1.create('arrow',[[0,0],v2],{color:'black', strokeWidth:1});
   var va2 = b1.create('arrow',[[0,0],v2],{strokeColor:'black', strokeWidth:1});


   var t = b1.create('text',[-8,5,function(){ return 'Matrix=<br>|'+b1.round(a.Value(),2)+' '+b1.round(b.Value(),2)+'|'+'<br>'+'|'+b1.round(c.Value(),2)+' '+b1.round(d.Value(),2)+'|';}]);
   var t = b1.create('text',[-8, 5,  
            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();
   b1.unsuspendUpdate();


   var t2 = b1.create('text',[7,5,
showTrace = false;
               function(){ return "&lambda; = |v'|/|v| = "  
var toggleTrace = function() {
                 + b1.round(
  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 HTML / JavaScript code ===
 
<source lang="HTML">
  <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
  <script id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
 
  <input type="button" id="toggleButton" value="Show trace" onClick="toggleTrace()">
</source>
 
<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});
 
  var t = b1.create('text',[-8, 5,
            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],[v2.X(),v2.Y()])/
                     JXG.Math.Geometry.distance([0,0],[v.X(),v.Y()]), 3
                     JXG.Math.Geometry.distance([0,0],[v.X(),v.Y()])
                   );}]);
                  ).toFixed(3)
                   + "\\]";}]);
   b1.unsuspendUpdate();
   b1.unsuspendUpdate();


</jsxgraph>
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>
 


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

Latest revision as of 08:20, 29 November 2023

This example uses MathJax.

The underlying HTML / JavaScript code

  <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
  <script id="MathJax-script" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>

  <input type="button" id="toggleButton" value="Show trace" onClick="toggleTrace()">
  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});

  var t = b1.create('text',[-8, 5, 
            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();
  }
};