EXAMPLES::
- sage: M = MatrixAlgebra(QQbar,RDF,2)
+ sage: M = MatrixAlgebra(2, QQbar,RDF)
sage: A = M.monomial((0,0,1)) + 4*M.monomial((0,1,1))
sage: A
+-----+-----+
EXAMPLES::
- sage: MatrixAlgebra(ZZ,ZZ,2).zero()
+ sage: MatrixAlgebra(2,ZZ,ZZ).zero()
+---+---+
| 0 | 0 |
+---+---+
EXAMPLES::
- sage: A = MatrixAlgebra(ZZ,ZZ,2)
+ sage: A = MatrixAlgebra(2,ZZ,ZZ)
sage: A([[1,2],[3,4]]).list()
[1, 2, 3, 4]
EXAMPLES::
- sage: M = MatrixAlgebra(ZZ,ZZ,2)([[1,2],[3,4]])
+ sage: M = MatrixAlgebra(2,ZZ,ZZ)([[1,2],[3,4]])
sage: M[0,0]
1
sage: M[0,1]
sage: entries = MatrixSpace(ZZ,2)
sage: scalars = ZZ
- sage: M = MatrixAlgebra(entries, scalars, 2)
+ sage: M = MatrixAlgebra(2, entries, scalars)
sage: I = entries.one()
sage: Z = entries.zero()
sage: M([[I,Z],[Z,I]]).trace()
sage: set_random_seed()
sage: entries = QuaternionAlgebra(QQ,-1,-1)
- sage: M = MatrixAlgebra(entries, QQ, 3)
+ sage: M = MatrixAlgebra(3, entries, QQ)
sage: M.random_element().matrix_space() == M
True
The existence of a unit element is determined dynamically::
- sage: MatrixAlgebra(ZZ,ZZ,2).one()
+ sage: MatrixAlgebra(2,ZZ,ZZ).one()
+---+---+
| 1 | 0 |
+---+---+
"""
Element = MatrixAlgebraElement
- def __init__(self, entry_algebra, scalars, n, prefix="A", **kwargs):
+ def __init__(self, n, entry_algebra, scalars, prefix="A", **kwargs):
category = MagmaticAlgebras(scalars).FiniteDimensional()
category = category.WithBasis()
sage: e = O.gens()
sage: e[2]*e[1]
-e3
- sage: A = MatrixAlgebra(O,QQ,2)
+ sage: A = MatrixAlgebra(2,O,QQ)
sage: A.product_on_basis( (0,0,e[2]), (0,0,e[1]) )
+-----+---+
| -e3 | 0 |
EXAMPLES::
- sage: A = MatrixAlgebra(QQbar, ZZ, 2)
+ sage: A = MatrixAlgebra(2, QQbar, ZZ)
sage: A.from_list([[0,I],[-I,0]])
+----+---+
| 0 | I |