半正交矩阵(定义)

半正交矩阵wiki

$$\begin{gathered} 如M=\left[\begin{array}{c}1\\ 0\end{array}\right],满足M^{t}M=I_{m,m}（A^{T}A=I\text{ or }A{A}^T=I.） \\ \left[\begin{array}{cc}1& 0\end{array}\right]\ast \left[\begin{array}{c}1\\ 0\end{array}\right]=1=I_{m,m} \\ orthogonalmatrix\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]=\left[\begin{array}{ccc}& {A_{2\ast 3}}_{正交阵的一半}& \\ g& h& i\end{array}\right]\Rightarrow \\ A\ast A^T=I_{2\ast 2} \end{gathered}$$

1.半正交矩阵是满秩的
2.$\Vert Mx{\Vert }_2=\Vert x{\Vert }_2$

In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasiorthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their constructions besides studying some of their properties.

pdf:Maths for Signals and Systems Linear Algebra in Engineering

半线性变换