Re: Aufgabe::Rechteckige Matrizen

[Nowak Robert <Robert.Nowak@XXXXXXX.at>]

Hallo Udo,

nach Bildung der Pseudoinversen erhält man mit den von Null
verschiedenen Elementen die Lottozahlen für den
21. Dezember, nur leider ...

LG Robert


On 06.12.2012 06:31, Udo und Susanne Krause wrote:
> Hallo,
>
> hier sind drei weitere Matrizen dieser Art, die Frage bleibt: welcher
> Art?
>
>
> {{1, 18, 17, 16, 9, 3, 5, 2, 4, 7, 6, 10, 15, 13, 12, 14, 8, 11},
>  {2, 1, 18, 17, 16, 11, 14, 4, 6, 3, 5, 7, 10, 9, 8, 12, 13, 15},
>  {4, 2, 1, 18, 17, 16, 9, 13, 5, 8, 6, 12, 7, 15, 11, 10, 14, 3},
>  {5, 3, 2, 1, 18, 4, 17, 16, 15, 14, 8, 7, 6, 13, 11, 9, 12, 10},
>  {9, 3, 2, 8, 18, 7, 6, 17, 16, 5, 15, 14, 4, 10, 13, 11, 12, 1},
>  {13, 18, 12, 17, 16, 11, 15, 6, 7, 10, 3, 8, 5, 1, 9, 14, 4, 2},
>  {15, 5, 6, 1, 14, 18, 13, 12, 17, 11, 10, 8, 16, 7, 2, 9, 3, 4},
>  {16, 7, 1, 6, 15, 18, 14, 17, 13, 12, 8, 10, 2, 9, 11, 3, 4, 5},
>  {17, 11, 4, 2, 3, 7, 5, 6, 1, 12, 10, 18, 9, 16, 14, 15, 13, 8},
>  {18, 17, 4, 7, 2, 3, 6, 5, 11, 1, 16, 10, 9, 8, 15, 13, 12, 14}}
>
>
>
> {{1, 16, 7, 4, 6, 3, 2, 11, 10, 5, 9, 8, 13, 12, 14, 15},
>  {2, 1, 15, 14, 12, 7, 6, 5, 4, 3, 10, 8, 9, 13, 11, 16},
>  {4, 2, 1, 16, 15, 14, 11, 13, 7, 5, 6, 9, 10, 12, 8, 3},
>  {5, 3, 2, 1, 16, 15, 4, 13, 14, 11, 6, 8, 7, 10, 9, 12},
>  {9, 3, 8, 2, 7, 6, 5, 15, 16, 4, 10, 14, 13, 11, 12, 1},
>  {13, 12, 16, 15, 11, 10, 9, 6, 5, 4, 7, 8, 14, 1, 3, 2},
>  {16, 15, 14, 13, 12, 11, 10, 9, 6, 5, 7, 8, 1, 2, 3, 4},
>  {14, 16, 13, 5, 1, 12, 7, 4, 6, 11, 15, 10, 3, 2, 9, 8},
>  {15, 4, 2, 5, 7, 3, 11, 6, 1, 10, 16, 13, 9, 8, 12, 14}}
>
>
>
> {{1, 14, 12, 11, 8, 6, 5, 4, 7, 9, 2, 3, 10, 13},
>  {2, 1, 7, 9, 10, 11, 4, 3, 6, 5, 8, 12, 13, 14},
>  {4, 2, 1, 10, 11, 8, 9, 5, 6, 7, 12, 13, 14, 3},
>  {5, 3, 8, 7, 1, 2, 9, 6, 10, 11, 12, 13, 14, 4},
>  {11, 9, 10, 3, 4, 5, 12, 13, 6, 7, 14, 2, 8, 1},
>  {9, 5, 4, 7, 6, 8, 10, 11, 12, 13, 14, 1, 3, 2},
>  {13, 9, 10, 11, 12, 14, 1, 6, 8, 5, 4, 2, 3, 7},
>  {12, 9, 13, 14, 11, 5, 1, 6, 10, 2, 3, 4, 7, 8}}
>
>
> Gruss
> Udo.
>
>> welche Eigenschaften haben die folgenden Matrizen gemeinsam?
>>
>> {{1, 10, 9, 12, 11, 3, 6, 4, 8, 7, 5, 2},
>>   {2, 1, 10, 11, 5, 12, 3, 7, 4, 8, 6, 9},
>>   {4, 2, 12, 1, 9, 3, 8, 11, 10, 6, 7, 5},
>>   {5, 4, 3, 2, 11, 1, 12, 9, 7, 8, 6, 10},
>>   {7, 8, 1, 5, 9, 4, 2, 12, 10, 3, 11, 6},
>>   {8, 9, 6, 12, 2, 3, 5, 4, 10, 11, 7, 1},
>>   {10, 12, 5, 6, 9, 11, 4, 8, 2, 7, 1, 3}}
>>
>>
>>
>> {{1, 10, 3, 6, 7, 9, 8, 4, 5, 2},
>>   {2, 1, 9, 7, 10, 8, 3, 5, 6, 4},
>>   {4, 2, 1, 10, 5, 9, 3, 7, 8, 6},
>>   {5, 3, 7, 6, 2, 1, 4, 10, 9, 8},
>>   {9, 4, 3, 10, 6, 1, 2, 7, 8, 5},
>>   {10, 8, 7, 5, 9, 4, 3, 6, 2, 1}}
>>
>>
>>
>> {{1, 8, 6, 4, 5, 7, 3, 2},
>>   {2, 1, 8, 3, 7, 6, 5, 4},
>>   {4, 2, 1, 3, 8, 7, 5, 6},
>>   {5, 8, 3, 4, 2, 6, 1, 7},
>>   {8, 4, 5, 6, 3, 7, 2, 1}}
>>
>>
>>
>> {{1, 6, 4, 3, 5, 2},
>>   {2, 1, 6, 4, 5, 3},
>>   {4, 2, 6, 3, 5, 1},
>>   {5, 3, 2, 6, 1, 4}}
>>
>>
>>
>> {{1, 4, 3, 2},
>>   {2, 1, 4, 3},
>>   {4, 2, 3, 1}}
>>
>>
>>
>> {{1, 2},
>>   {2, 1}}
>>
>>
>>
>> {{1}}
>>
>>
>>
>> Mit den besten Grüssen
>> Udo.
>
>
>


-- 
DI (FH) Robert Nowak
IMS Nanofabrication AG
Austria, 1020 Wien, Schreygasse 3
Phone: +43 1 2144894-32
Fax:   +43 1 2144894-99
mailto:robert.nowak@XXXXXXX.at
http://www.ims.co.at

begin:vcard
fn:Robert Nowak
n:Nowak;Robert
org:IMS Nanofabrication AG
adr:;;Schreygasse 3;Wien;;1020;Austria
email;internet:robert.nowak@XXXXXXX.at
tel;work:+43 1 2144894 32
tel;fax:+43 1 2144894 99
url:http://www.ims.co.at
version:2.1
end:vcard