Esempio: funzioni per norme e determinanti della matrice

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Esempio: funzioni per norme e determinanti della matrice

1. Definire una matrice quadrata.

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2. Impostare gli elementi della matrice su nomi di variabile generici.

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3. Utilizzare la funzione norm1 per trovare la norma L1 della matrice M.

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In alternativa, trovare la norma L1 calcolando il valore massimo delle somme di colonna assolute di M.

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4. Utilizzare la funzione norm2 per trovare la norma L2 della matrice M.

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In alternativa, utilizzare la funzione svds per trovare il singolo valore assoluto più grande della matrice M.

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La funzione svds restituisce un vettore di singoli valori ordinati, in modo che il valore superiore sia il singolo valore più grande della matrice M.

5. Utilizzare la funzione norme per trovare la norma euclidea della matrice M.

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In alternativa, calcolare manualmente la radice quadrata della somma dei quadrati assoluti della matrice M.

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6. Utilizzare la funzione normi per trovare la norma infinita della matrice M.

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In alternativa, utilizzare la funzione max per calcolare manualmente il valore massimo delle somme di riga assolute della matrice M.

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          <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
            <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
          </id>
        </apply>
      </apply>
    </define>
    <resultFormat xml:lang="it">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="it" />
    </resultFormat>
  </math>
</region>

Fare clic per copiare questa espressione

<region id="ID0EQQKMB" actualWidth="155.11333333333334" actualHeight="27.791200000000003" top="1209.6000000000001" left="38.400000000000006" xml:lang="it" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="70" xml:lang="it">
    <define xml:lang="it" xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve" xml:lang="it">
        <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
      </id>
      <apply xml:lang="it">
        <plus xml:lang="it" />
        <apply xml:lang="it">
          <plus xml:lang="it" />
          <apply xml:lang="it">
            <absval xml:lang="it" />
            <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
              <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
            </id>
          </apply>
          <apply xml:lang="it">
            <absval xml:lang="it" />
            <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
              <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
            </id>
          </apply>
        </apply>
        <apply xml:lang="it">
          <absval xml:lang="it" />
          <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
            <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
          </id>
        </apply>
      </apply>
    </define>
    <resultFormat xml:lang="it">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="it" />
    </resultFormat>
  </math>
</region>

Fare clic per copiare questa espressione

<region id="ID0ECRKMB" actualWidth="252.23666666666671" actualHeight="27.791200000000003" top="1248.0000000000002" left="38.400000000000006" xml:lang="it" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="72" xml:lang="it">
    <define xml:lang="it" xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve" xml:lang="it">
        <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">N<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">i</Subscript></Span>
      </id>
      <eval xml:lang="it">
        <apply xml:lang="it">
          <id labels="FUNCTION" xml:space="preserve" xml:lang="it" label-is-contextual="true">max</id>
          <sequence xml:lang="it">
            <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
              <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
            </id>
            <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
              <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
            </id>
            <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
              <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ARS<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
            </id>
          </sequence>
        </apply>
        <unitOverride xml:lang="it">
          <placeholder xml:lang="it" />
        </unitOverride>
      </eval>
    </define>
    <resultFormat xml:lang="it">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="it" />
    </resultFormat>
  </math>
</region>

7. Utilizzare la funzione det per trovare il determinante della matrice M.

Fare clic per copiare questa espressione

In alternativa, calcolare manualmente il determinante della matrice M.

Fare clic per copiare questa espressione

<region id="ID0EJUKMB" actualWidth="490.83" actualHeight="27.791200000000003" top="1401.6000000000001" left="38.400000000000006" xml:lang="it" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="76" xml:lang="it">
    <define xml:lang="it" xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve" xml:lang="it">DET</id>
      <eval xml:lang="it">
        <apply xml:lang="it">
          <plus xml:lang="it" />
          <apply xml:lang="it">
            <minus xml:lang="it" />
            <apply xml:lang="it">
              <mult xml:lang="it" />
              <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
              </id>
              <parens xml:lang="it">
                <apply xml:lang="it">
                  <minus xml:lang="it" />
                  <apply xml:lang="it">
                    <mult xml:lang="it" />
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                      <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                      <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                  </apply>
                  <apply xml:lang="it">
                    <mult xml:lang="it" />
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                      <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                      <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                    </id>
                  </apply>
                </apply>
              </parens>
            </apply>
            <apply xml:lang="it">
              <mult xml:lang="it" />
              <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
              </id>
              <parens xml:lang="it">
                <apply xml:lang="it">
                  <minus xml:lang="it" />
                  <apply xml:lang="it">
                    <mult xml:lang="it" />
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                      <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                      <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                  </apply>
                  <apply xml:lang="it">
                    <mult xml:lang="it" />
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                      <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                      <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                    </id>
                  </apply>
                </apply>
              </parens>
            </apply>
          </apply>
          <apply xml:lang="it">
            <mult xml:lang="it" />
            <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
              <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
            </id>
            <parens xml:lang="it">
              <apply xml:lang="it">
                <minus xml:lang="it" />
                <apply xml:lang="it">
                  <mult xml:lang="it" />
                  <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                    <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                  </id>
                  <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                    <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                  </id>
                </apply>
                <apply xml:lang="it">
                  <mult xml:lang="it" />
                  <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                    <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                  </id>
                  <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                    <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                  </id>
                </apply>
              </apply>
            </parens>
          </apply>
        </apply>
        <unitOverride xml:lang="it">
          <placeholder xml:lang="it" />
        </unitOverride>
      </eval>
    </define>
    <resultFormat xml:lang="it">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="it" />
    </resultFormat>
  </math>
</region>

8. Utilizzare la funzione norm per trovare la norma di un vettore contenente gli elementi della colonna 0 della matrice M.

Fare clic per copiare questa espressione

<region id="ID0EZWKMB" actualWidth="109.26666666666668" actualHeight="69.37360000000001" top="1497.6000000000001" left="38.400000000000006" xml:lang="it" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="78" xml:lang="it">
    <define xml:lang="it" xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve" xml:lang="it">v</id>
      <eval xml:lang="it">
        <matrix rows="3" cols="1" xml:lang="it">
          <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
            <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
          </id>
          <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
            <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
          </id>
          <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
            <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
          </id>
        </matrix>
        <unitOverride xml:lang="it">
          <placeholder xml:lang="it" />
        </unitOverride>
      </eval>
    </define>
  </math>
</region>

Fare clic per copiare questa espressione

In alternativa, calcolare manualmente la norma del vettore v.

Fare clic per copiare questa espressione

<region id="ID0EIYKMB" actualWidth="207.04933364629747" actualHeight="36.780453040075308" top="1632.0000000000002" left="38.400000000000006" xml:lang="it" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="82" xml:lang="it">
    <define xml:lang="it" xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve" xml:lang="it">N</id>
      <eval xml:lang="it">
        <apply xml:lang="it">
          <nthRoot xml:lang="it" />
          <placeholder xml:lang="it" />
          <apply xml:lang="it">
            <plus xml:lang="it" />
            <apply xml:lang="it">
              <plus xml:lang="it" />
              <apply xml:lang="it">
                <pow xml:lang="it" />
                <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                  <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                </id>
                <real xml:lang="it">2</real>
              </apply>
              <apply xml:lang="it">
                <pow xml:lang="it" />
                <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                  <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                </id>
                <real xml:lang="it">2</real>
              </apply>
            </apply>
            <apply xml:lang="it">
              <pow xml:lang="it" />
              <id labels="VARIABLE" xml:space="preserve" xml:lang="it" label-is-contextual="true">
                <Span xml:lang="it" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="it" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
              </id>
              <real xml:lang="it">2</real>
            </apply>
          </apply>
        </apply>
        <unitOverride xml:lang="it">
          <placeholder xml:lang="it" />
        </unitOverride>
      </eval>
    </define>
    <resultFormat xml:lang="it">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="it" />
    </resultFormat>
  </math>
</region>