Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
INPUT:
•V - vector space (space of degree self.ncols()) that contains the image of self.
See Also:
restrict(), restrict_domain()
EXAMPLES:
sage: A = matrix(QQ,3,[1..9])
sage: V = (QQ^3).span([[1,2,3], [7,8,9]]); V
Vector space of degree 3 and dimension 2 over Rational Field
Basis matrix:
[ 1 0 -1]
[ 0 1 2]
sage: z = vector(QQ,[1,2,5])
sage: B = A.restrict_codomain(V); B
[1 2]
[4 5]
[7 8]
sage: z*B
(44, 52)
sage: z*A
(44, 52, 60)
sage: 44*V.0 + 52*V.1
(44, 52, 60)
restrict_domain(V)
Compute the matrix relative to the basis for V on the domain obtained by restricting self to V, but not
changing the codomain of the matrix. This is the matrix whose rows are the images of the basis for V.
INPUT:
•V - vector space (subspace of ambient space on which self acts)
See Also:
restrict()
EXAMPLES:
sage: V = QQ^3
sage: A = matrix(QQ,3,[1,2,0, 3,4,0, 0,0,0])
sage: W = V.subspace([[1,0,0], [1,2,3]])
sage: A.restrict_domain(W)
[1 2 0]
[3 4 0]
sage: W2 = V.subspace_with_basis([[1,0,0], [1,2,3]])
sage: A.restrict_domain(W2)
[ 1 2 0]
[ 7 10 0]
right_eigenmatrix()
Return matrices D and P, where D is a diagonal matrix of eigenvalues and P is the corresponding matrix
where the columns are corresponding eigenvectors (or zero vectors) so that self*P = P*D.
EXAMPLES:
sage: A = matrix(QQ,3,3,range(9)); A
[0 1 2]
[3 4 5]
[6 7 8]
231