α^2A=|D00,D01,D02,D03,D04,α|
|D10,D11,D12,D13,D14,α|
|D20,D21,D22,D23,D24,α|
|D30,D31,D32,D33,D34,α|
|D40,D41,D42,D43,D44,α|
| α, α, α, α, α,0|
まず,第1行を他の行から引いて
|D00,D01 ,D02 ,D03 ,D04 ,α|
|D10,D11-D01,D12-D02,D13-D03,D14-D04,0|
|D20,D21-D01,D22-D02,D23-D03,D24-D04,0|
|D30,D31-D01,D32-D02,D33-D03,D34-D04,0|
|D40,D41-D01,D42-D02,D43-D03,D44-D04,0|
| α, α-D01, α-D02, α-D03, α-D04,-α|
さらに第2列~第n列を第1列に加えれば
|D00+D0x+ α,D01 ,D02 ,D03 ,D04 0,|
|D10+D1x-D0x,D11-D01,D12-D02,D13-D03,D14-D03,0|
|D20+D2x-D0x,D21-D01,D22-D02,D23-D03,D24-D03,0|
|D30+D3x-D0x,D31-D01,D32-D02,D33-D03,D34-D03,0|
|D40+D4x-D0x,D41-D01,D42-D02,D43-D03,D44-D03,0|
| 4α-D0x, α-D01, α-D02, α-D03, α-D03,-α|
α=D0x/4とおけば
-α^2|D11-D01,D12-D02,D13-D03,D14-D04|
|D21-D01,D22-D02,D23-D03,D24-D04|
|D31-D01,D32-D02,D33-D03,D34-D04|
|D41-D01,D42-D02,D43-D03,D44-D04|
E44=-D04+(D14-D04)(D41-D01)/D01
-α^2|D11-D01,D12-D02,D13-D03,0|
|D21-D01,D22-D02,D23-D03,D24-D04|
|D31-D01,D32-D02,D33-D03,D34-D04|
| 0,D42-D02,D43-D03,E44|
E33=-D03+(D13-D03)(D31-D01)/D01
-α^2|D11-D01,D12-D02,0 ,0|
|D21-D01,D22-D02,D23-D03,D24-D04|
| 0,D32-D02,E33 ,D34-D04|
| 0,D42-D02,D43-D03,E44|
F44=E44+(D24-D04)(D42-D02)/D02
-α^2|D11-D01,D12-D02,0 ,0|
|D21-D01,D22-D02,D23-D03,,0|
| 0,D32-D02,E33 ,D34-D04|
| 0, 0,D43-D03,F44|
E22=-D02+(D12-D02)(D21-D01)/D01
-α^2|D11-D01,0 ,0 ,0|
| 0,E22 ,D23-D03,,0|
| 0,D32-D02,E33 ,D34-D04|
| 0, 0,D43-D03,F44|
F33=E33-(D23-D03)(D32-D02)/E22
α^2|D01,0 ,0 ,0|
| 0,E22 ,0 ,0|
| 0,0 ,F33 ,D34-D04|
| 0,0 ,D43-D03,F44|
G44=F44-(D34-D04)(D43-D03)/F33
α^2|D01,0 ,0 ,0|
| 0,E22,0 ,0|
| 0,0 ,F33,0|
| 0,0 ,0 ,G44|
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