Good matrices of even order の編集 - Araya PukiWiki

Good matrices of even order の編集 - Araya PukiWiki

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#contents

We generated good matrices in Jennifer Seberry's research. We can generated good matrices of even order.

* define [#n416bd60]

A,B,C,D:four (1,-1) matrices,order m.

+ NM^T=MN^T (N,M in A,B,C,D)
+ AA^T+BB^T+CC^T+DD^T=4mI
+ (A-I)^T=-(A-I),B^T=B,C^T=C,D^T=D

If A,B,C,D with all properties , then will be called good matrices.

* good matrices [#n416bd60]

good matrices of even order are as follows:

|order|A|B|C|D|
|2|&ref(good_2_a.txt,,,data);|&ref(good_2_b.txt,,,data);|&ref(good_2_c.txt,,,data);|&ref(good_2_d.txt,,,data);|
|4|&ref(good_4_a.txt,,,data);|&ref(good_4_b.txt,,,data);|&ref(good_4_c.txt,,,data);|&ref(good_4_d.txt,,,data);|
|6|&ref(good_6_a.txt,,,data);|&ref(good_6_b.txt,,,data);|&ref(good_6_c.txt,,,data);|&ref(good_6_d.txt,,,data);|
|8|&ref(good_8_a.txt,,,data);|&ref(good_8_b.txt,,,data);|&ref(good_8_c.txt,,,data);|&ref(good_8_d.txt,,,data);|

* reference [#n416bd60]

Jennifer Seberry:「Wiliamson matrices of even order」Combinatorial Mathematics vol.403 Lecture Notes in Mathematics,Springer-Verlag,pp.132-142,1974
http://www.uow.edu.au/~jennie/WEB/WEB69-93/max/037_1974.pdf

* author [#n416bd60]

Takumi Watanabe 2013 2/15

タイムスタンプを変更しない

#contents

We generated good matrices in Jennifer Seberry's research. We can generated good matrices of even order.

* define [#n416bd60]

A,B,C,D:four (1,-1) matrices,order m.

+ NM^T=MN^T (N,M in A,B,C,D)
+ AA^T+BB^T+CC^T+DD^T=4mI
+ (A-I)^T=-(A-I),B^T=B,C^T=C,D^T=D

If A,B,C,D with all properties , then will be called good matrices.

* good matrices [#n416bd60]

good matrices of even order are as follows:

|order|A|B|C|D|
|2|&ref(good_2_a.txt,,,data);|&ref(good_2_b.txt,,,data);|&ref(good_2_c.txt,,,data);|&ref(good_2_d.txt,,,data);|
|4|&ref(good_4_a.txt,,,data);|&ref(good_4_b.txt,,,data);|&ref(good_4_c.txt,,,data);|&ref(good_4_d.txt,,,data);|
|6|&ref(good_6_a.txt,,,data);|&ref(good_6_b.txt,,,data);|&ref(good_6_c.txt,,,data);|&ref(good_6_d.txt,,,data);|
|8|&ref(good_8_a.txt,,,data);|&ref(good_8_b.txt,,,data);|&ref(good_8_c.txt,,,data);|&ref(good_8_d.txt,,,data);|

* reference [#n416bd60]

Jennifer Seberry:「Wiliamson matrices of even order」Combinatorial Mathematics vol.403 Lecture Notes in Mathematics,Springer-Verlag,pp.132-142,1974
http://www.uow.edu.au/~jennie/WEB/WEB69-93/max/037_1974.pdf

* author [#n416bd60]

Takumi Watanabe 2013 2/15

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