#1 02. 05. 2013 03:47
- stuart clark
- Příspěvky: 1015
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Max. and Min. of Determinant
(1) The Max. and Min. value of a 
order Determinant whose element are taken from the set 
(2) The Max. and Min. value of order Determinant whose element are taken from the set 
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#2 02. 05. 2013 22:47 — Editoval Pavel (02. 05. 2013 23:30)
Re: Max. and Min. of Determinant
is the maximal value of a determinant then 
is its minimal value. It suffices to switch any two rows - the sign of the determinant will be changed.
![$A=[0,0,0]$](/mathtex/2a/2ac9f4ef993700011562c96f456b0783.gif "kopírovat do textarea")
, ![$B=[a,b,c]$](/mathtex/07/07bf19323ee501220c2a8cc44ffa094a.gif "kopírovat do textarea")
, ![$C=[d,e,f]$](/mathtex/28/284863ed81026fe2892413ddc3116604.gif "kopírovat do textarea")
and ![$D=[g,h,i]$](/mathtex/0c/0cc2351fd2cb18550c177e1c19af02ca.gif "kopírovat do textarea")
, if the determinant is positive. If it is negative, then the volume differs just in the sign 
.
, 
, 
such that entries of 
then we double coordinates of points B,C and D![$
A=[0,0,0],\ B=[2,2,2],\ C=[-2,2,2],\ D=[0,-2,2].
$](/mathtex/0d/0da0c6ee601e2457b84da817a18c6fa7.gif "kopírovat do textarea")
Backslash je v TeXu tak důležitý jako nekonečno při dělení nulou v tělesech charakteristiky 0.
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#3 07. 05. 2013 04:41
- stuart clark
- Příspěvky: 1015
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Re: Max. and Min. of Determinant
Thanks pavel
But I Did not understand the line
It is not difficult to find out that one of several solutions is![$
A=[0,0,0],\ B=[1,1,1],\ C=[-1,1,1],\ D=[0,-1,1].
$](/mathtex/39/391499b15476c424f4ff85353925d443.gif "kopírovat do textarea")
The volume is 
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