Diferencia entre revisiones de «Matemáticas/Álgebra Lineal/Espacios Vectoriales 2»

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Línea 79:
<math>A =
\begin{pmatrix}
a_{11} & a_{2112} & \ldots & a_{n11n} \\
a_{1221} & a_{22} & \ldots & a_{n22n} \\
\vdots & \vdots & \vdots & \vdots \\
a_{1ji1} & a_{2ji2} & \ldots & a_{njin} \\
\vdots & \vdots & \vdots & \vdots \\
a_{1mm1} & a_{2mm2} & \ldots & a_{nmmn}
\end{pmatrix},\ni A \in M_{m,n}(\mathbb{K})
</math>
Línea 101:
<math>C =
\begin{pmatrix}
a_{11} & a_{2112} & \ldots & a_{n11n} \\
a_{1221} & a_{22} & \ldots & a_{n22n} \\
\vdots & \vdots & \vdots & \vdots \\
a_{1jj1} & a_{2jj2} & \ldots & a_{njjn} \\
\vdots & \vdots & \vdots & \vdots \\
a_{1nn1} & a_{2nn2} & \ldots & a_{nn}
\end{pmatrix},\ni C \in M_{m,n}(\mathbb{K})
</math>
Línea 130:
\begin{pmatrix}
a_{11} \\
a_{1221} \\
\vdots \\
a_{1ji1} \\
\vdots \\
a_{1mm1}
\end{pmatrix},\ni D \in M_{m,1}(\mathbb{K})
</math>
Línea 165:
<math>A =
\begin{pmatrix}
a_{11} & a_{2112} & \ldots & a_{n11n} \\
a_{1221} & a_{22} & \ldots & a_{n22n} \\
\vdots & \vdots & \vdots & \vdots \\
a_{1ji1} & a_{2ji2} & \ldots & a_{njin} \\
\vdots & \vdots & \vdots & \vdots \\
a_{1mm1} & a_{2mm2} & \ldots & a_{nmmn}
\end{pmatrix}, B =
\begin{pmatrix}
b_{11} & b_{2112} & \ldots & b_{n11n} \\
b_{1221} & b_{22} & \ldots & b_{n22n} \\
\vdots & \vdots & \vdots & \vdots \\
b_{1ji1} & b_{2ji2} & \ldots & b_{njin} \\
\vdots & \vdots & \vdots & \vdots \\
b_{1mm1} & b_{2mm2} & \ldots & b_{nmmn}
\end{pmatrix}, \ni A,B \in M_{m,n}(\mathbb{K})
</math>
Línea 184:
<math>A+B =
\begin{pmatrix}
a_{11}+b_{11} & a_{2112}+b_{2112} & \ldots & a_{n11n}+b_{n11n} \\
a_{1221}+b_{1221} & a_{22}+b_{22} & \ldots & a_{n22n}+b_{n22n}\\
\vdots & \vdots & \vdots & \vdots \\
a_{1ji1}+b_{1ji1} & a_{2ji2}+b_{2ji2} & \ldots & a_{njin}+b_{njin} \\
\vdots & \vdots & \vdots & \vdots \\
a_{1mm1}+b_{1mm1} & a_{2mm2}+b_{2mm2} & \ldots & a_{nmmn}+b_{nmmn}
\end{pmatrix}, \ni [A+B]\in M_{m,n}(\mathbb{K})
</math>
Línea 199:
<math>\alpha \cdot A =
\begin{pmatrix}
\alpha \cdot a_{11} & \alpha \cdot a_{2112} & \ldots & \alpha \cdot a_{n11n} \\
\alpha \cdot a_{1221} & \alpha \cdot a_{22} & \ldots & \alpha \cdot a_{n22n} \\
\vdots & \vdots & \vdots & \vdots \\
\alpha \cdot a_{1ji1} & \alpha \cdot a_{2ji2} & \ldots & \alpha \cdot a_{njin} \\
\vdots & \vdots & \vdots & \vdots \\
\alpha \cdot a_{1mm1} & \alpha \cdot a_{2mm2} & \ldots & \alpha \cdot a_{nmmn}
\end{pmatrix}, \ni [\alpha \cdot A] \in M_{m,n}(\mathbb{K})
</math>
Línea 254:
<math>A =
\begin{pmatrix}
b_{11} & b_{2112} & \ldots & b_{n11n} \\
b_{1221} & b_{22} & \ldots & b_{n22n} \\
\vdots & \vdots & \vdots & \vdots \\
b_{1ji1} & b_{2ji2} & \ldots & b_{njin} \\
\vdots & \vdots & \vdots & \vdots \\
b_{1mm1} & b_{2mm2} & \ldots & b_{nmmn}
\end{pmatrix}, A^{T}=
\begin{pmatrix}