> restart;
> with(LinearAlgebra):
> A := Matrix(3,2,[[1,2],[3,4],[5,6]]);

                                 [1    2]
                                 [      ]
                            A := [3    4]
                                 [      ]
                                 [5    6]

> B := <<a,b>|<c,d>>;

                                 [a    c]
                            B := [      ]
                                 [b    d]

> A . B;

                       [ a + 2 b      c + 2 d ]
                       [                      ]
                       [3 a + 4 b    3 c + 4 d]
                       [                      ]
                       [5 a + 6 b    5 c + 6 d]

> v := Vector[row]([alpha, Xi, Chi]);

                        v := [alpha, Xi, Chi]

> A . v;
Error, (in LinearAlgebra:-MatrixVectorMultiply) invalid input:
LinearAlgebra:-MatrixVectorMultiply expects its 2nd argument, v, to be
of type Vector[column] but received Vector[row](3, [...], datatype =
anything)

> v . A;

            [alpha + 3 Xi + 5 Chi, 2 alpha + 4 Xi + 6 Chi]

> ?identity
> I3 := Matrix(3,3,shape=identity);

                               [1    0    0]
                               [           ]
                         I3 := [0    1    0]
                               [           ]
                               [0    0    1]

> I2 := Matrix(2,2,shape=identity);

                                  [1    0]
                            I2 := [      ]
                                  [0    1]

> A;

                               [1    2]
                               [      ]
                               [3    4]
                               [      ]
                               [5    6]

> B;

                               [a    c]
                               [      ]
                               [b    d]

> I3 . A;

                               [1    2]
                               [      ]
                               [3    4]
                               [      ]
                               [5    6]

> A . I2;

                               [1    2]
                               [      ]
                               [3    4]
                               [      ]
                               [5    6]

> fibo[0] := Vector([0,1]);

                                       [0]
                            fibo[0] := [ ]
                                       [1]

> Fibo := <<0,1>|<1,1>>;

                                   [0    1]
                           Fibo := [      ]
                                   [1    1]

> for i from 1 to 10 do fibo[i] := Fibo . fibo[i-1]; od;

                                       [1]
                            fibo[1] := [ ]
                                       [1]


                                       [1]
                            fibo[2] := [ ]
                                       [2]


                                       [2]
                            fibo[3] := [ ]
                                       [3]


                                       [3]
                            fibo[4] := [ ]
                                       [5]


                                       [5]
                            fibo[5] := [ ]
                                       [8]


                                      [ 8]
                           fibo[6] := [  ]
                                      [13]


                                      [13]
                           fibo[7] := [  ]
                                      [21]


                                      [21]
                           fibo[8] := [  ]
                                      [34]


                                      [34]
                           fibo[9] := [  ]
                                      [55]


                                       [55]
                           fibo[10] := [  ]
                                       [89]

> Fibo^10;

                              [34    55]
                              [        ]
                              [55    89]

> Fibopow[0]:=Fibo;

                                      [0    1]
                        Fibopow[0] := [      ]
                                      [1    1]

> for i from 1 to 10 do Fibopow[i] := Fibopow[i-1]^2; od;

                                      [1    1]
                        Fibopow[1] := [      ]
                                      [1    2]


                                      [2    3]
                        Fibopow[2] := [      ]
                                      [3    5]


                                     [13    21]
                       Fibopow[3] := [        ]
                                     [21    34]


                                   [610     987]
                     Fibopow[4] := [           ]
                                   [987    1597]


                                [1346269    2178309]
                  Fibopow[5] := [                  ]
                                [2178309    3524578]


                         [ 6557470319842    10610209857723]
           Fibopow[6] := [                                ]
                         [10610209857723    17167680177565]


  Fibopow[7] :=

        [155576970220531065681649693 , 251728825683549488150424261]

        [251728825683549488150424261 , 407305795904080553832073954]


  Fibopow[8] :=

        [87571595343018854458033386304178158174356588264390370 ,

        141693817714056513234709965875411919657707794958199867]

        [141693817714056513234709965875411919657707794958199867 ,

        229265413057075367692743352179590077832064383222590237]


  Fibopow[9] :=

        [277459222893057168553384709160828150293488720296478308619\

        14852073402148308000613611082094085891168867554589 , 448938\
        4531330994297807729816066062664618188362388623979126969446\

        6661322268805744081870933775586567858979269]

        [448938453133099429780772981606606266461818836238862397912\

        69694466661322268805744081870933775586567858979269 , 726397\
        6760261565983341576907674344167553075565353407065318454654\

        0063470576806357692953027861477736726533858]


  Fibopow[10] :=

        [278529355069959292393881241266809350935330735212370380691\
        3182668987369503203465183625616759613324452749958549669966\
        8821911178954250152084554694037312726521582408256284848181\

        31485544230827304940519132195299466733282 , 450669963367781\
        9813104383235728886049367860596218604830803023149600030645\
        7087213962487926091410303962448732665803450112195302093674\
        2558101987106764609420026228520234665586889971108924677841\

        3354004103631553925405243]

        [450669963367781981310438323572888604936786059621860483080\
        3023149600030645708721396248792609141030396244873266580345\
        0112195302093674255810198710676460942002622852023466558688\

        99711089246778413354004103631553925405243 , 729199318437741\
        2737043195648396979558721167948342308637716205818587400148\
        9121865798744093687543548489948318162503118934106481047924\
        4078947534047137736685242052602797514068703119663347760571\

        8294523235826853392138525]

> read("C:\\cygwin/home/erich/www/courses/LinAlgebra/Maple/initlib.mpl")
> ;

  libname := "C:\cygwin/home/erich/www/courses/LinAlgebra/Maple",

        "C:\Program Files\Maple 12/lib"

> with(RefPkg);

       [E_I, E_II, E_III, MyDet, MyInverse, MySolve, Ref, XRef]

> Ref(A);

                          Searching column 1


                  Added row 1 times , -3,  to row 2


                              [1     2]
                              [       ]
                              [0    -2]
                              [       ]
                              [5     6]


                  Added row 1 times , -5,  to row 3


                              [1     2]
                              [       ]
                              [0    -2]
                              [       ]
                              [0    -4]


                          Searching column 2


                  Added row 2 times , -2,  to row 3


                              [1     2]
                              [       ]
                              [0    -2]
                              [       ]
                              [0     0]


                              [1     2]
                              [       ]
                              [0    -2]
                              [       ]
                              [0     0]

> ?userinfo
> infolevel['RefPkg']:=3;

                        infolevel[RefPkg] := 3

> A1 := Matrix([[a,b],[c,d]]);

                                  [a    b]
                            A1 := [      ]
                                  [c    d]

> B1 := Matrix([[alpha,beta],[gamma,delta]]);

                              [alpha    beta ]
                        B1 := [              ]
                              [gamma    delta]

> C1 := Matrix([[Psi,Lambda],[Theta,Phi]]);

                             [ Psi     Lambda]
                       C1 := [               ]
                             [Theta     Phi  ]

> M1:=map(expand,(A1 . B1) . C1);

  M1 :=

        [Psi a alpha + Psi b gamma + Theta a beta + Theta b delta ,

        Lambda a alpha + Lambda b gamma + Phi a beta + Phi b delta]

        [Psi c alpha + Psi d gamma + Theta c beta + Theta d delta ,

        Lambda c alpha + Lambda d gamma + Phi c beta + Phi d delta]

> M2:=map(expand,A1 . (B1 . C1));

  M2 :=

        [Psi a alpha + Psi b gamma + Theta a beta + Theta b delta ,

        Lambda a alpha + Lambda b gamma + Phi a beta + Phi b delta]

        [Psi c alpha + Psi d gamma + Theta c beta + Theta d delta ,

        Lambda c alpha + Lambda d gamma + Phi c beta + Phi d delta]

> equal(M1, M2);

  equal(

        [Psi a alpha + Psi b gamma + Theta a beta + Theta b delta ,

        Lambda a alpha + Lambda b gamma + Phi a beta + Phi b delta]

        [Psi c alpha + Psi d gamma + Theta c beta + Theta d delta ,

        Lambda c alpha + Lambda d gamma + Phi c beta + Phi d delta],

        [Psi a alpha + Psi b gamma + Theta a beta + Theta b delta ,

        Lambda a alpha + Lambda b gamma + Phi a beta + Phi b delta]

        [Psi c alpha + Psi d gamma + Theta c beta + Theta d delta ,

        Lambda c alpha + Lambda d gamma + Phi c beta + Phi d delta])

>