Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[0|0]
[3|0]
sage: m.apply_map(lambda x: x+1)
[1|1]
[4|1]
apply_morphism(phi)
Apply the morphism phi to the coefficients of this sparse matrix.
The resulting matrix is over the codomain of phi.
INPUT:
•phi - a morphism, so phi is callable and phi.domain() and phi.codomain() are defined. The codomain
must be a ring.
OUTPUT: a matrix over the codomain of phi
EXAMPLES:
sage: m = matrix(ZZ, 3, range(9), sparse=True)
sage: phi = ZZ.hom(GF(5))
sage: m.apply_morphism(phi)
[0 1 2]
[3 4 0]
[1 2 3]
sage: m.apply_morphism(phi).parent()
Full MatrixSpace of 3 by 3 sparse matrices over Finite Field of size 5
augment(right, subdivide=False)
Return the augmented matrix of the form:
[self | right].
EXAMPLES:
sage: M = MatrixSpace(QQ, 2, 2, sparse=True)
sage: A = M([1,2, 3,4])
sage: A
[1 2]
[3 4]
sage: N = MatrixSpace(QQ, 2, 1, sparse=True)
sage: B = N([9,8])
sage: B
[9]
[8]
sage: A.augment(B)
[1 2 9]
[3 4 8]
sage: B.augment(A)
[9 1 2]
[8 3 4]
A vector may be augmented to a matrix.
sage: A = matrix(QQ, 3, 4, range(12), sparse=True)
sage: v = vector(QQ, 3, range(3), sparse=True)
sage: A.augment(v)
[ 0 1 2 3 0]
[ 4 5 6 7 1]
[ 8 9 10 11 2]
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