Математическое моделирование при ортогонализации матриц. Черный А.А. - 7 стр.

                             x m2 n =
                                         1 2n
                                         N
                                                (      2n
                                              x ma + x mb      2n
                                                           + x mc       2n
                                                                    + x md       2n
                                                                            + x me   )
                                                                                     ;

                               x m2 r =
                                         1 2r
                                         N
                                                (      2r
                                              x ma + x mb      2r
                                                           + x mc       2r
                                                                    + x md       2r
                                                                            + x me   )
                                                                                     ;

                               x m2 s =
                                         1 2s
                                         N
                                                (      2s
                                              x ma + x mb      2s
                                                           + x mc       2s
                                                                    + x md       2s
                                                                            + x me   )
                                                                                     ;

                         x mn+ r =
                                       N
                                        (
                                       1 n+ r
                                           x ma + x mbn+ r     n+ r
                                                           + x mc        n+ r
                                                                     + x md        n+r
                                                                               + x me    )
                                                                                         ;

                          x mn+ s =
                                       N
                                        (
                                       1 n+ s
                                           x ma + x mbn+ s     n+ s
                                                           + x mc        n+ s
                                                                     + x md        n+ s
                                                                               + x me    )
                                                                                         ;

                        x mn+ w =
                                      N
                                        (
                                      1 n+ w
                                          x ma + x mbn+ w      n+ w
                                                           + x mc         n+ w
                                                                     + x md         n+ w
                                                                                + x me      ;)
                           x mr + s =
                                       N
                                            (
                                        1 r +s        r+s
                                            x ma + x mb        r +s
                                                           + x mc        r+s
                                                                     + x md        r+s
                                                                              + x me    ;)
                        x mr + w =
                                      N
                                        (
                                       1 r+w         r+w
                                           x ma + x mb         r+w
                                                           + x mc         r+w
                                                                     + x md         r+w
                                                                               + x me      ; )
                        x ms + w =
                                      N
                                        (
                                       1 s+w
                                           x ma + x mbs+w      s+w
                                                           + x mc         s+w
                                                                     + x md         s+w
                                                                               + x me      ; )
                                xm =
                                         1
                                         N
                                                (
                                             x ma + x mb + x mc + x md + x me ;      )
      Ортогональность матрицы планирования (см.табл.1) обеспечивается в
том случае, если
xmna + xmnb + x mne + xmnd + xmnc = 0 ,
x mra + x mrb + x mre + x mrd + x mrc = 0 ,
x msa + x msb + x mse + x msd + x msc = 0 ,
xmwa + xmwb + xmwe + xmwd + xmwc = 0 ,
x mna ⋅ x mra + x mnb ⋅ x mrb + x mnc ⋅ x mrc + x mnd ⋅ x mrd + x mne ⋅ x mre = 0 ,
xmna ⋅ xmsa + x mnb ⋅ x msb + x mnc ⋅ x msc + xmnd ⋅ x msd + x mne ⋅ xmse = 0 ,
x mna ⋅ x mwa + x mnb ⋅ x mwb + x mnc ⋅ x mwc + x mnd ⋅ x mwd + x mne ⋅ x mwe = 0 ,
x mra ⋅ x msa + x mrb ⋅ x msb + x mrc ⋅ x msc + x mrd ⋅ x msd + x mre ⋅ x mse = 0 ,
xmra ⋅ x mwa + xmrb ⋅ xmwb + x mrc ⋅ x mwc + x mrd ⋅ xmwd + x mre ⋅ x mwe = 0 ,
x msa ⋅ x mwa + x msb ⋅ x mwb + x msc ⋅ x mwc + x msd ⋅ x mwd + x mse ⋅ x mwe = 0 .
      После подстановки в уравнения системы значений слагаемых и сомно-
жителей, замены получаемых сумм средними арифметическими величинами
и сокращения одинаковых величин получается система из десяти уравнений,

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