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Question Number 143718 by cherokeesay last updated on 17/Jun/21

Commented by TheHoneyCat last updated on 17/Jun/21

$H i, w h a t d o y o u m e a n b y^{″} ∣ B ∣^{″} ?$ $i t l o o k s l i k e y o u a r e t a l k i n g a b o u t a n o r m b u t w h i c h o n e ?$
Commented by TheHoneyCat last updated on 17/Jun/21

$Q_{2}$ $E D = [\begin{matrix} 1 & X \\ X & 1 \end{matrix}] \times [\begin{matrix} 2 & y \\ 1 & - y \end{matrix}] = [\begin{matrix} 2 + X & (1 - X) y \\ 2 X + 1 & (X - 1) y \end{matrix}]$ $D E = [\begin{matrix} 2 & y \\ 1 & - y \end{matrix}] \times [\begin{matrix} 1 & X \\ X & 1 \end{matrix}] = [\begin{matrix} 2 + y X & 2 X + y \\ 1 - y X & X - y \end{matrix}]$ $the first term (m_{0, 0}) imposes y = 1 to get D E = E D$ $the one under (m_{1, 0}) imposes 2 X + 1 = 1 - X \Leftrightarrow 3 X = 0 \Leftrightarrow X = 0$ $checking (m_{0, 1}) with these conditions, we get 1 = - 1$ $which is obviously false$ $so \forall (X, y) \in C^{2} E D \neq D E$
Commented by Olaf_Thorendsen last updated on 17/Jun/21

$In some countries, France for example,$ $\det (B) is sometimes noted ∣ B ∣ .$
Commented by TheHoneyCat last updated on 17/Jun/21

$well, I think this notation only concers the expressions$ $it is used to do explicit calculations or block calculations$ $At least {that}^{'} s how we do it in my School (which is in France of course, otherwise I would not have any idea)$ $we use \det M when M is not explicit$ $But maybe is is used is some other places$
Commented by TheHoneyCat last updated on 17/Jun/21

$\det (B) = (- 2 i) (6 + 2 i) - 4 \times 1$ $= - 12 i + 4 - 4$ $= - 12 i$
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