Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
TESTS:
sage: m = matrix([])
sage: m.apply_map(lambda x: x*x) == m
True
sage: m.apply_map(lambda x: x*x, sparse=True).parent()
Full MatrixSpace of 0 by 0 sparse matrices over Integer Ring
apply_morphism(phi)
Apply the morphism phi to the coefficients of this dense 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))
sage: phi = ZZ.hom(GF(5))
sage: m.apply_morphism(phi)
[0 1 2]
[3 4 0]
[1 2 3]
sage: parent(m.apply_morphism(phi))
Full MatrixSpace of 3 by 3 dense matrices over Finite Field of size 5
We apply a morphism to a matrix over a polynomial ring:
sage: R. = QQ[]
sage: m = matrix(2, [x,x^2 + y, 2/3*y^2-x, x]); m
[ x x^2 + y]
[2/3*y^2 - x x]
sage: phi = R.hom([y,x])
sage: m.apply_morphism(phi)
[ y y^2 + x]
[2/3*x^2 - y y]
transpose()
Returns the transpose of self, without changing self.
EXAMPLES: We create a matrix, compute its transpose, and note that the original matrix is not changed.
sage: M = MatrixSpace(QQ, 2)
sage: A = M([1,2,3,4])
sage: B = A.transpose()
sage: print B
[1 3]
[2 4]
sage: print A
[1 2]
[3 4]
.T is a convenient shortcut for the transpose:
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