eigenvectors |
Syntax |
eigenvectors(M: MAT, X: RINGELEM): LIST of RECORD |
Description |
Example |
/**/ Use R ::= QQ[x]; /**/ M := mat([[1,2,3],[4,5,6],[7,8,9]]); /**/ eigenvectors(M, x); [record[MinPoly := x, eigenspace := matrix(QQ, [[-1], [2], [-1]])], record[MinPoly := x^2 -15*x -18, eigenspace := [[1, (1/8)*x +1/4, (1/4)*x -1/2]]] ] /**/ M := mat([[0,2,0,0],[1,0,0,0],[0,0,0,2],[0,0,1,0]]); eigenvectors(M, x); -- two irrational eigenvalues, each with eigenspace of dimension 2 [record[MinPoly := x^2 -2, eigenspace := [[1, (1/2)*x, 0, 0], [0, 0, 1, (1/2)*x]]]] |