Übung: Matrizenmultiplikation

Das Skalarprodukt
Gegeben sind zwei Vektoren der gleichen Dimension: [br][math]\vec v=\begin{pmatrix}v_1\\v_2\\\vdots\\v_n\end{pmatrix}[/math] und [math]\vec w=\begin{pmatrix}w_1\\w_2\\\vdots\\w_n\end{pmatrix}[/math][br]Dann ist das Skalarprodukt dieser beiden Vektoren definiert, als[br][math]\text{\Large{$\boxed{\vec v \bullet \vec w = v_1\cdot w_1 +v_2\cdot w_2 + ... + v_n\cdot w_n}$}}[/math][br]Tatsächlich wird für dieses Produkt oft ein etwas dickerer Punkt oder ein ähnliches Zeichen verwendet, um es von der Multiplikation zweier Zahlen zu unterscheiden. Das Besondere ist, dass hier zwei Vektoren multipliziert werden, [b]dass das Ergebnis aber [i]kein Vektor[/i] ist[/b], sondern eine Zahl. Da man eine einfache Zahl in der Mathematik auch einen [i]Skalar[/i] nennt, heißt dieses Produkt [color=#980000][b]Skalarprodukt[/b][/color].
Multiplizieren von Matrizen
[size=150][color=#980000]Bei der Multiplikation von Matrizen werden Skalarprodukte gebildet, aus den Zeilenvektoren der linken Matrix und den Spaltenvektoren der rechten Matrix.[br][br][b]Eine Multiplikation von Matrizen ist nur dann möglich, wenn die Anzahl der Spalten der linken Matrix gleich der Anzahl der Zeilen der rechten Matrix ist.[br][br]Eine [math]\text{\Large{$\fgcolor{#980000}{(l\times \mathbf m)}$}}[/math]-Matrix kann also mit einer [math]\text{\Large{$\fgcolor{#980000}{(\mathbf m\times n)}$}}[/math]-Matrix multipliziert werden. Das Ergebnis ist dann eine [/b][/color][/size][size=150][color=#980000][b][math]\text{\Large{$\fgcolor{#980000}{(l\times n)}$}}[/math]-Matrix.[/b][/color][/size][br][br][math]\text{\LARGE{$\fgcolor{#980000}{ \begin{array}{ccccc}[br]\mathbf A & \cdot & \mathbf B &=&\mathbf C \\[br](\fgcolor{#009800}{\mathbf l} \times \mathbf { m})&&(\mathbf m \times \fgcolor{#000098}{\mathbf n})&&( \fgcolor{#009800}{\mathbf l} \times \fgcolor{#000098}{\mathbf n})[br]\end{array}}$}}[br][/math]
Ein Zahlenbeispiel
Man kann zu Beginn ein Matrizenprodukt auch mit dem folgenden Schema berechnen.[br]Mit ein Bisschen Übung wird das Schema später überflüssig.[br]Berechnet werden soll: [math]\left(\begin{array}{rr}3&8\\\\-8&10\\\\0&5\end{array}\right)\cdot \left(\begin{array}{rr} 2& 7 \\4 &5\end{array}\right)=[/math][br] 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[/img][br][br]Damit ist das Ergebnis:[br][math]\left(\begin{array}{rr}3&8\\\\-8&10\\\\0&5\end{array}\right)\cdot \left(\begin{array}{rr} 2& 7 \\4 &5\end{array}\right)=\begin{pmatrix}38&61\\24&-6\\20&25\end{pmatrix}[/math]

Information: Übung: Matrizenmultiplikation