Maple/矩阵与矢量

矢量

v1:=Vector([1,2,3,4]);

Vector(4, {(1) = 1, (2) = 2, (3) = 3, (4) = 4});

$\left[\begin{array}{c}1\\ 2\\ 3\\ 4\end{array}\right].$

v2:=Vector([5,6,7,8]);

$\left[\begin{array}{c}5\\ 6\\ 7\\ 8\end{array}\right].$

v1+v2;

$\left[\begin{array}{c}6\\ 8\\ 10\\ 12\end{array}\right].$

10v1+10v2;

$\left[\begin{array}{c}60\\ 80\\ 100\\ 120\end{array}\right].$

v3:=v2^*

$\left[\begin{array}{cccc}5& 6& 7& 8\end{array}\right].$

矩阵

A5:=Matrix(5,5, (i,j)-> j+(i-1)*5);

$\left[\begin{array}{c}\\ 1& 2& 3& 4& 5\\ 6& 7& 8& 9& 10\\ 11& 12& 13& 14& 15\\ 16& 17& 18& 19& 20\\ 21& 22& 23& 24& 25\end{array}\right].$

A6=A5^*

$\left[\begin{array}{c}\\ 1& 6& 11& 16& 21\\ 2& 7& 12& 17& 22\\ 3& 8& 13& 18& 23\\ 4& 9& 18& 19& 24\\ 5& 10& 15& 20& 25\end{array}\right].$

v6:=Vector([1,2,3,4,5])

$\left[\begin{array}{c}1\\ 2\\ 3\\ 4\\ 5\end{array}\right].$

MatrixVectorMultiply(A5,v6);

$\left[\begin{array}{c}\\ 55\\ 130\\ 205\\ 280\\ 355\end{array}\right]$

MatrixScalarMultiply(A5, A6);

$\left[\begin{array}{c}\\ 55& 130& 205& 280& 355\\ 130& 330& 530& 730& 930\\ 205& 530& 855& 1180& 1505\\ 280& 730& 1180& 1630& 2080\\ 355& 930& 1505& 2080& 2655\end{array}\right].$