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4.12.4 matrix operations
+
- addition with matrix or poly; the polynomial is converted into a diagonal
matrix
-
- negation or subtraction with matrix or poly
(the first operand is expected to be a matrix);
the polynomial is converted into a diagonal matrix
*
- multiplication with matrix or poly; the polynomial is converted into a
diagonal matrix
/
- division by poly
==, <>, !=
- comparators
- matrix_expression
[ int_expression, int_expression ]
- is a matrix entry, where the first index indicates the row and the
second the column
Example:
| | ring r=32003,x,dp;
matrix A[3][3] = 1,3,2,5,0,3,2,4,5; // define a matrix
print(A); // nice printing of small matrices
==> 1,3,2,
==> 5,0,3,
==> 2,4,5
A[2,3]; // matrix entry
==> 3
A[2,3] = A[2,3] + 1; // change entry
A[2,1..3] = 1,2,3; // change 2nd row
print(A);
==> 1,3,2,
==> 1,2,3,
==> 2,4,5
matrix E[3][3]; E = E + 1; // the unit matrix
matrix B =x*E - A;
print(B);
==> x-1,-3, -2,
==> -1, x-2,-3,
==> -2, -4, x-5
// the same (but x-A does not work):
B = -A+x;
print(B);
==> x-1,-3, -2,
==> -1, x-2,-3,
==> -2, -4, x-5
det(B); // the characteristic polynomial of A
==> x3-8x2-2x-1
A*A*A - 8 * A*A - 2*A == E; // Cayley-Hamilton
==> 1
vector v =[x,-1,x2];
A*v; // multiplication of matrix and vector
==> _[1,1]=2x2+x-3
==> _[2,1]=3x2+x-2
==> _[3,1]=5x2+2x-4
matrix m[2][2]=1,2,3;
print(m-transpose(m));
==> 0,-1,
==> 1,0
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