[[-0.283+0.959j, 0.001-0.005j], [0.459-0.423j, -0.777+0.089j]]和其转置的积
时间: 2024-01-24 19:18:04 浏览: 29
首先,我们需要求出该矩阵的转置矩阵:
$$
\begin{bmatrix}
-0.283+0.959j & 0.001-0.005j\\
0.459-0.423j & -0.777+0.089j
\end{bmatrix}^T
=
\begin{bmatrix}
-0.283+0.959j & 0.459-0.423j\\
0.001-0.005j & -0.777+0.089j
\end{bmatrix}
$$
然后,我们将其两个矩阵相乘:
$$
\begin{bmatrix}
-0.283+0.959j & 0.001-0.005j\\
0.459-0.423j & -0.777+0.089j
\end{bmatrix}
\begin{bmatrix}
-0.283+0.959j & 0.459-0.423j\\
0.001-0.005j & -0.777+0.089j
\end{bmatrix}
=
\begin{bmatrix}
(-0.283+0.959j)(-0.283+0.959j)+(0.001-0.005j)(0.459-0.423j) & (-0.283+0.959j)(0.459-0.423j)+(0.001-0.005j)(-0.777+0.089j)\\
(0.459-0.423j)(-0.283+0.959j)+(-0.777+0.089j)(0.001-0.005j) & (0.459-0.423j)(0.459-0.423j)+(-0.777+0.089j)(-0.777+0.089j)
\end{bmatrix}
$$
计算后得到:
$$
\begin{bmatrix}
1.102-1.342j & -0.190-0.622j\\
-0.190-0.622j & 0.846+1.961j
\end{bmatrix}
$$
因此,该矩阵与其转置的积为:
$$
\begin{bmatrix}
1.102-1.342j & -0.190-0.622j\\
-0.190-0.622j & 0.846+1.961j
\end{bmatrix}
$$