Definition 24 identity matrix/multiplicative unity, \(\delta \quad \hat{=}\) Kronecker-symbol
| \[ \tilde I=\underbrace{\left.\left(\begin{array}{cc}\begin{array}{cc}1&\\&1\end{array}&0\\0&\begin{array}{cc}\ddots&\\ &1\end{array}\end{array}\right)\right\}}_{N}N\qquad N\times N,\mbox{quadratic}\quad \tilde I = \left(\delta_{jk}\right) \qquad \delta_{jk} = \left\{\begin{array}{ll}0&\mbox{if $j\neq k$}\\\\1&\mbox{if $j=k$}\end{array}\right.\] |
\begin{eqnarray*}\tilde A\tilde I&=&\tilde A=\tilde I\tilde A\\ \tilde A\cdot\tilde 0&=&\tilde0\cdot\tilde A=\tilde0 \mbox{ (trivial)}\\ \left(\tilde A\tilde B\right)^\top&=&\tilde{B}^\top\tilde{A}^\top\\ \left(\tilde{A}\tilde{B}\right)^+&=&\tilde{B}^+\tilde{A}^+\end{eqnarray*}
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© J. Carstensen (Math for MS)