Multiplikation einer Matrix mit der Einheitsmatrix

Lesedauer: 2 min | Vorlesen | Autor: Dr. Volkmar Naumburger

\(A \cdot I = \left( {\begin{array}{*{20}{c} }{ {a_{11} } }&{ {a_{12} } }&{...}&{ {a_{1K} } }\\{ {a_{21} } }&{ {a_{22} } }&{...}&{ {a_{2K} } }\\{...}&{...}&{ {a_{ik} } }&{...}\\{ {a_{I1} } }&{ {a_{I2} } }&{...}&{ {a_{IK} } }\end{array} } \right).\left( {\begin{array}{*{20}{c} }1&0&{...}&0\\0&1&{...}&0\\{...}&{...}&1&{...}\\0&0&{...}&1\end{array} } \right) = \left( {\begin{array}{*{20}{c} }{ {a_{11} } }&{ {a_{12} } }&{...}&{ {a_{1K} } }\\{ {a_{21} } }&{ {a_{22} } }&{...}&{ {a_{2K} } }\\{...}&{...}&{ {a_{ik} } }&{...}\\{ {a_{I1} } }&{ {a_{I2} } }&{...}&{ {a_{IK} } }\end{array} } \right) = \left( A \right)\) Gl. 164

Indice I = K!

Die Multiplikation mit der Einheitsmatrix verändert die Matrix nicht!

Weiterhin gilt:

\(A \cdot I = I \cdot A \) Gl. 165

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