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4.9.4 matrix operations
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+ addition with matrix or poly; the poly is converted into a diagonal matrix
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- negation or subtraction with matrix or poly; the poly is converted into a diagonal matrix
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* multiplication with matrix or poly; the poly is converted into a diagonal matrix
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/ division by poly
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==,<>,!= comparison
- 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 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 |