Adjungierte Matrix « 0,1,2,3,…

Adjungierte Matrix

June 24, 2007

Adjungierte Matrix (conjugate matrix)

$\begin{matrix} A*=A^H & = & \bar{A}^T \\ \bar{z} & = & a-b\cdot i \\ \langle Av, w\rangle & = & \langle v, A^*\,w\rangle, v, w \in\Bbb K^n \\ \Bbb K =\Bbb R & \rightarrow & A^*=A^T \\\end{matrix}$

$A=A* \Longleftrightarrow$ selbstadjungiert, symmetrisch; hermitesch

$\begin{matrix}\left(A + B\right)^* &=& A^* + B^*\\rA)^* &=& \overline{r}A^*\\\left(AB\right)^* &=& B^*A^*\\\left(A^*\right)^* &=& A\\\left(A^{-1}\right)^* &=& \left(A^*\right)^{-1}\\det(A^*) &=&\overline{\det(A)}\\ trace(A^*) &=& \overline{trace(A)}\end{matrix}$

$adj(A) = \tilde A^T = \begin{pmatrix} \tilde a_{11} & \tilde a_{21} & \cdots & \tilde a_{n1}\\ \tilde a_{12} & \tilde a_{22} & & \tilde a_{n2}\\ \vdots & & \ddots & \vdots\\ \tilde a_{1n} & \tilde a_{2n} & \cdots & \tilde a_{nn}\end{pmatrix}$

Posted in Lineare Algebra |

One comment

Wie kannst du die Formeln so gut in WordPress formatieren? Das sieht klasse aus.
by mathebuch June 24, 2007 at 8:33 pm

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