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796 APPENDIX A A MAPLE Primer

In an entirely analogous way, we can carry out vector operations in spherical coordinates.
First, change to this coordinate system:
SetCoordinates(‘spherical’[rho,theta,phi]);
For the MAPLE command

∗
Gradient(rho sin(phi)∧2) cos(theta/2));
∗
returns the gradient in spherical coordinates:

1
1 1 2 1 2sin(φ)cos 2 θ cos(φ)
2
sin(φ) cos θ e ρ − sin(φ) sin θ e θ + e φ .
2 2 2 sin(θ)
Some vector operations can also be carried out using the linear algebra package, which is
discussed next. Details are available in the MAPLE Help package.

A.4 Matrix Manipulations

To work with matrices, load the linear algebra package, using

with(linalg);
Again, the semicolon will give a list of the subroutines. To avoid the list, end this command with
a colon.
There are many ways to enter a matrix. One way is to enter the dimension and the rows. For
example,

Matrix(4,2,[[-1,3],[6,1],[6,5],[-1,-2]]);
enters the 4 × 2matrix
⎛ ⎞
−1 3
6 1
⎜ ⎟
⎜ ⎟ .
⎝ 6
5 ⎠
−1 −2
To give this matrix the name K, enter
K:=Matrix(4,2,[[-1,3],[6,1],[6,5],[-1,-2]]);
For the inverse of a nonsingular matrix A which has been entered, use

inverse(A);
For the rank of a matrix L (which need not be square), use
rank(L);
For the determinant of square A, use

det(A);
Multiply a matrix A by a scalar c by
∗
c A;
Add two n × m matrices as we would expect using
A+B;

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October 14, 2010 15:43 THM/NEIL Page-796 27410_24_appA_p789-800