半正交矩阵wiki

如 M = [ 1 0 ] , 满 足 M t M = I m , m （ A T A = I  or  A A T = I .   ） [ 1 0 ] ∗ [ 1 0 ] = 1 = I m , m o r t h o g o n a l   m a t r i x [ a b c d e f g h i ] = [   A 2 ∗ 3 正 交 阵 的 一 半 g h i ] ⇒ A ∗ A T = I 2 ∗ 2 如M=\begin{bmatrix}1\\0\end{bmatrix},满足M^tM=I_{m,m}（A^T A = I \text{ or } A A^T = I. \,）\\ \begin{bmatrix}1&0\end{bmatrix}*\begin{bmatrix}1\\0\end{bmatrix}=1=I_{m,m}\\ orthogonal \ matrix\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix} = \begin{bmatrix} \ & {A_{2*3}}_{正交阵的一半}\\g&h&i\end{bmatrix} \Rightarrow \\ A*A^T=I_{2*2} 如M=[10​],满足MtM=Im,m​（ATA=I or AAT=I.）[1​0​]∗[10​]=1=Im,m​orthogonal matrix⎣⎡​adg​beh​cfi​⎦⎤​=[ g​A2∗3​正交阵的一半​h​i​]⇒A∗AT=I2∗2​

1.半正交矩阵是满秩的
2. ∥ M x ∥ 2 = ∥ x ∥ 2 \|Mx\|_2 = \|x\|_2 ∥Mx∥2​=∥x∥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.

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