Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
True
sage: [A[:i,:i].determinant() for i in range(1,A.nrows()+1)]
[2, 2, 6]
TESTS:
If the base ring lacks a conjugate method, it will be assumed to not be Hermitian and thus symmetric.
If the base ring does not make sense as a subfield of the reals, then this routine will fail since comparison
to zero is meaningless.
sage: F. = FiniteField(5^3)
sage: a.conjugate()
Traceback (most recent call last):
...
AttributeError: ’sage.rings.finite_rings.element_givaro.FiniteField_givaroElement’
object has no attribute ’conjugate’
sage: A = matrix(F,
... [[ a^2 + 2*a, 4*a^2 + 3*a + 4, 3*a^2 + a, 2*a^2 + 2*a + 1],
... [4*a^2 + 3*a + 4, 4*a^2 + 2, 3*a, 2*a^2 + 4*a + 2],
... [ 3*a^2 + a, 3*a, 3*a^2 + 2, 3*a^2 + 2*a + 3],
... [2*a^2 + 2*a + 1, 2*a^2 + 4*a + 2, 3*a^2 + 2*a + 3, 3*a^2 + 2*a + 4]])
sage: A.is_positive_definite()
Traceback (most recent call last):
...
TypeError: cannot convert computations from
Finite Field in a of size 5^3 into real numbers
AUTHOR:
•Rob Beezer (2012-05-24)
is_scalar(a=None)
Return True if this matrix is a scalar matrix.
INPUT
•base_ring element a, which is chosen as self[0][0] if a = None
OUTPUT
•whether self is a scalar matrix (in fact the scalar matrix aI if a is input)
EXAMPLES:
sage: m = matrix(QQ,2,range(4))
sage: m.is_scalar(5)
False
sage: m = matrix(QQ,2,[5,0,0,5])
sage: m.is_scalar(5)
True
sage: m = matrix(QQ,2,[1,0,0,1])
sage: m.is_scalar(1)
True
sage: m = matrix(QQ,2,[1,1,1,1])
sage: m.is_scalar(1)
False
is_similar(other, transformation=False)
Returns True if self and other are similar, i.e. related by a change-of-basis matrix.
INPUT:
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