Question-143718

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