Before starting matrix calculations, load the linear algebra package:
> with(linalg):
Vectors and matrices are created with the commands vector and matrix respectively. A vector (which is not a special case of a matrix) is regarded as a column vector by multiplication. Some examples:
> A:=matrix([[4,34],[-a,sqrt(2)]]): > a12:=A[1,2]: > v:=vector([x,-12]): > w:=v[2]:
The command array can also be used to create a matrix.
Whenever doing matrix calculations the function evalm has
to be applied. Matrix multiplication is written &* which has to be
surrounded by spaces. Multiplication with a scalar is called *
Thus to perform , where the operands are matrices, you type
> A:=evalm(2* transpose(B) &* C + D);
The characteristic polynomial of A with s as variable is obtained by > charpoly(A,s);and > eigenvals(A); gives the eigenvalues of A as an expression sequence. Example:
> B:=matrix([[1, sqrt(2)], [-ln(3), 3]]):
> evalf([eigenvals(B)],5);
[2. + .74404 I, 2. - .74404 I]