Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
The vector of constants, b, can be given in a variety of forms, so long as it coerces to a vector over the
same base ring as the coefficient matrix.
sage: A=matrix(CDF, 5, [1/(i+j+1) for i in range(5) for j in range(5)])
sage: A.solve_left([1]*5) # rel tol 1e-11
(5.0, -120.0, 630.0, -1120.0, 630.0)
TESTS:
A degenerate case.
sage: A = matrix(RDF, 0, 0, [])
sage: A.solve_left(vector(RDF,[]))
()
The coefficent matrix must be square.
sage: A = matrix(RDF, 2, 3, range(6))
sage: b = vector(RDF, [1,2,3])
sage: A.solve_left(b)
Traceback (most recent call last):
...
ValueError: coefficient matrix of a system over RDF/CDF must be square, not 2 x 3
The coefficient matrix must be nonsingular.
sage: A = matrix(RDF, 5, range(25))
sage: b = vector(RDF, [1,2,3,4,5])
sage: A.solve_left(b)
Traceback (most recent call last):
...
LinAlgError: singular matrix
The vector of constants needs the correct degree.
sage: A = matrix(RDF, 5, range(25))
sage: b = vector(RDF, [1,2,3,4])
sage: A.solve_left(b)
Traceback (most recent call last):
...
TypeError: vector of constants over Real Double Field incompatible with matrix over Real Dou
The vector of constants needs to be compatible with the base ring of the coefficient matrix.
sage: F. = FiniteField(27)
sage: b = vector(F, [a,a,a,a,a])
sage: A.solve_left(b)
Traceback (most recent call last):
...
TypeError: vector of constants over Finite Field in a of size 3^3 incompatible with matrix o
With a coefficient matrix over RDF, a vector of constants over CDF can be accomodated by converting the
base ring of the coefficient matrix.
sage: A = matrix(RDF, 2, range(4))
sage: b = vector(CDF, [1+I,2])
sage: A.solve_left(b)
Traceback (most recent call last):
...
TypeError: vector of constants over Complex Double Field incompatible with matrix over Real
390 Chapter 19. Dense matrices using a NumPy backend.