転置行列

,

1.1

\(A=\left(a_{i j}\right)=\left[\begin{array}{rrrr}
a_{11} & a_{12} & \cdots & a_{1 n} \\
a_{21} & a_{22} & \cdots & a_{2 n} \\
& & \cdots & \\
a_{m 1} & a_{m 2} & \cdots & a_{m n}
\end{array}\right]\)

\({ }^t A=\left(a_{j i}\right)=\left[\begin{array}{cccc}
a_{11} & a_{21} & \cdots & a_{m 1} \\
a_{12} & a_{22} & \cdots & a_{m 2} \\
& & \cdots & \\
a_{1 n} & a_{2 n} & \cdots & a_{m n}
\end{array}\right]\)

1.2

\({ }^t(A+B)={ }^t A+{ }^t B\)

1.3

\({ }^t(A B)={ }^t B^t A\)