Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: R. = QuaternionAlgebra(-1, -1)
sage: A = matrix(R, 2, [1,i,j,k])
sage: B = matrix(R, 2, [i,i,i,i])
sage: A.elementwise_product(B)
[ i -1]
[-k j]
sage: B.elementwise_product(A)
[ i -1]
[ k -j]
Input that is not a matrix will raise an error.
sage: A = random_matrix(ZZ,5,10,x=20)
sage: A.elementwise_product(vector(ZZ, [1,2,3,4]))
Traceback (most recent call last):
...
TypeError: operand must be a matrix, not an element of Ambient free module of rank 4 over th
Matrices of different sizes for operands will raise an error.
sage: A = random_matrix(ZZ,5,10,x=20)
sage: B = random_matrix(ZZ,10,5,x=40)
sage: A.elementwise_product(B)
Traceback (most recent call last):
...
TypeError: incompatible sizes for matrices from: Full MatrixSpace of 5 by 10 dense matrices
Some pairs of rings do not have a common parent where multiplication makes sense. This will raise an
error.
sage: A = matrix(QQ, 3, range(6))
sage: B = matrix(GF(3), 3, [2]*6)
sage: A.elementwise_product(B)
Traceback (most recent call last):
...
TypeError: no common canonical parent for objects with parents: ’Full MatrixSpace of 3 by 2
We illustrate various combinations of sparse and dense matrices. Notice how if base rings are unequal,
both operands must be sparse to get a sparse result.
sage: A = matrix(ZZ, 5, range(30), sparse=False)
sage: B = matrix(ZZ, 5, range(30), sparse=True)
sage: C = matrix(QQ, 5, range(30), sparse=True)
sage: A.elementwise_product(C).is_dense()
True
sage: B.elementwise_product(C).is_sparse()
True
sage: A.elementwise_product(B).is_dense()
True
sage: B.elementwise_product(A).is_dense()
True
TESTS:
Implementation for dense and sparse matrices are different, this will provide a trivial test that they are
working identically.
sage: A = random_matrix(ZZ, 10, x=1000, sparse=False)
sage: B = random_matrix(ZZ, 10, x=1000, sparse=False)
sage: C = A.sparse_matrix()
168 Chapter 7. Base class for matrices, part 2