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  <region id="0" left="18" top="18" width="185" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p bold="true">Vektoren und Matrizen</p>
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    <text lang="eng">
      <p bold="true">Vectors and Matrices</p>
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  <region id="1" left="18" top="54" width="674" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
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      <p>Matrizen sind rechteckige Anordnungen von mathematischen Ausdrücken. Eine Matrix 
mit m Zeilen und n Spalten heißt m x n-Matrix. Vektoren im Sinne der linearen
Algebra sind Matrizen mit einer einzigen Spalte.</p>
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    <text lang="eng">
      <p>Matrices are rectangular arrays of expressions. A matrix consisting of m rows and 
n columns is called a m x n matrix. Vectors are matrices which consist of a single 
column. </p>
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        <e type="operand">1</e>
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        <e type="operand" style="string">A11</e>
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        <e type="operand">A</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
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        <e type="operand">33</e>
        <e type="operand" style="unit">m</e>
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    <math>
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        <e type="operand">A</e>
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      <result action="numeric">
        <e type="operand" style="string">A11</e>
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        <e type="operand">33</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">3</e>
        <e type="operand">4</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="8">mat</e>
        <e type="operand">5</e>
        <e type="operand">6</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="8">mat</e>
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    <picture>
      <raw format="png" encoding="base64"> </raw>
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  <region id="8" left="189" top="216" width="109" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
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        <e type="operand">A</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
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        <e type="operand">2</e>
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  <region id="9" left="351" top="216" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>A[2;2</p>
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    <text lang="eng">
      <p>A[2,2</p>
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  <region id="10" left="405" top="216" width="53" height="24" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p> Leer </p>
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    <text lang="eng">
      <p>Space</p>
    </text>
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  <region id="11" left="459" top="216" width="45" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>[2;2</p>
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    <text lang="eng">
      <p>[2,2=</p>
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  <region id="12" left="18" top="288" width="715" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Matrizenelemente können durch Adress-Indizes angesprochen werden, die mit der eckigen 
Klammer [ erzeugt werden. Ein zweiter Index wird mit dem Argumenttrennzeichen 
(Semikolon) erzeugt.</p>
    </text>
    <text lang="eng">
      <p>Matrix elements are adressed by adress indices. These are created using the [ symbol.
A second index is created by typing the argument separator character (komma).</p>
    </text>
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  <region id="13" left="18" top="333" width="251" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Details zur Indizierung siehe</p>
    </text>
    <text lang="eng">
      <p>For details on index handling see </p>
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  <region id="14" left="324" top="333" width="45" height="24" color="#c0c0c0" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="el.sm">el()</p>
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  <region id="15" left="18" top="387" width="242" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section matrix create.sm">Matrizen interaktiv erzeugen</p>
    </text>
    <text lang="eng">
      <p href="Section matrix create.sm">Create matrices interactively</p>
    </text>
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  <region id="16" left="18" top="405" width="275" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section matrix createfunctions.sm">Matrizen mit Funktionen erzeugen</p>
    </text>
    <text lang="eng">
      <p href="Section matrix createfunctions.sm">Functions which create matrices</p>
    </text>
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  <region id="17" left="18" top="423" width="284" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section matrix operations.sm">Rechnen mit Matrizen und Vektoren</p>
    </text>
    <text lang="eng">
      <p href="Section matrix operations.sm">Matrix operations</p>
    </text>
  </region>
  <region id="18" left="18" top="441" width="391" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section matrix operations symbolic.sm">Symbolisches Rechnen mit Matrizen und Vektoren</p>
    </text>
    <text lang="eng">
      <p href="Section matrix operations symbolic.sm">Symbolic matrix operations</p>
    </text>
  </region>
  <region id="19" left="18" top="459" width="218" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section matrix handling.sm">Manipulation von Matrizen</p>
    </text>
    <text lang="eng">
      <p href="Section matrix handling.sm">Matrix Handling</p>
    </text>
  </region>
  <region id="20" left="18" top="477" width="176" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section matrix sorting.sm">Suchen und Sortieren</p>
    </text>
    <text lang="eng">
      <p href="Section matrix sorting.sm">Seаrching and Sorting</p>
    </text>
  </region>
  <region id="21" left="18" top="495" width="275" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section matrix elementwise.sm">Funktionen elementweise anwenden</p>
    </text>
    <text lang="eng">
      <p href="Section matrix elementwise.sm">Elementwise application of functions</p>
    </text>
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  <region id="22" left="18" top="531" width="390" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Section matrix least square.sm">Beispiel: Methode der kleinsten Fehlerquadrate</p>
    </text>
    <text lang="eng">
      <p href="Section matrix least square.sm">Example: Least square fit</p>
    </text>
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  <region id="23" left="18" top="549" width="267" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Example Matrix joinblocks.sm">Beispiel: Blockmatrix verbinden</p>
    </text>
    <text lang="eng">
      <p href="Example Matrix joinblocks.sm">Example: Join submatrices of a block matrix</p>
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  <region id="24" left="18" top="585" width="94" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Mathematik.sm">Mathematik</p>
    </text>
    <text lang="eng">
      <p href="Mathematik.sm">Mathematics</p>
    </text>
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  <region id="25" left="18" top="603" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
    </text>
    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
    </text>
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  <region id="26" left="18" top="639" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2014-01-19 22:49:58 +0100 (So, 19. Jan 2014) $ </p>
    </text>
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