Creating Matrices and Vectors in Maple
Version .8 for Maple V R7.
Load pointers to functions in the linear algebra package.
Warning, the protected names norm and trace have been redefined and unprotected
Entering a matrix as a list of lists.
> A1 := matrix([ [1,2,3], [4,5,6], [7,8,9] ]);
Enter a vector - will be viewed as a column vector.
> v1 := vector([1, 2, 3]);
We could now multiply A1 times v1 by evalm(A1 &* v1);
Another form of the vector call is vector(3,1) producing a column vector of dim 3 with
initial entries 1.
> v2 := vector(3,1);
Enter a 2 by 3 matrix with entries taken in row major order from the list.
> A2 := matrix(2,3,[x,y,z,w,u,v]);
Enter a 2 by 2 matrix with all entries initialized to 0.
> A3 := matrix(2,2,0);
One can also define a function of row and column indices to initialize a matrix.
> f := (i,j) -> j * x^(i + j);
> A4 := matrix(2,2,f);
A 1 by 3 matrix; i.e. a row vector.
> v3 := matrix(1,3,4);
Another form of a column vector.
> v4 := matrix(2,1,[ 5, 6]);
Matrices can be partially specified:
> A4 := matrix(2,3,[[x,y,z]]);
And then updated with a for loop.
for j from 1 to 3 do
A4[2,j] := x * y^j:
Nested loops are also possible to update all entries of a matrix.
Matrices can be stacked horizontally.
> A5 := augment(A2,A4);
A6 := stackmatrix(A2,v3);
One can delete a range of rows from a matrix.
(Use delcols for columns.)
Block diagonal or diagonal matrices can also be easily generated.
> A6 := diag(lambda_1, lambda_2);
(These commands can be used with more than two arguments.)
> A7 := diag(A6,A6):
One can create a 5 x 5 banded matrix by:
A 3 by 3 Jordan block with diagonal entry 5 can be generated by:
Extract a submatrix using rows 1..3 of A1 and columns 2..3.
> A8 := submatrix(A1,1..3,2..3);
Extract rows and columns as vectors.
> row(A8,2); col(A8,1);