Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: P, L, U = A.LU()
sage: P
[0.0 0.0 0.0 0.0 1.0]
[1.0 0.0 0.0 0.0 0.0]
[0.0 0.0 1.0 0.0 0.0]
[0.0 0.0 0.0 1.0 0.0]
[0.0 1.0 0.0 0.0 0.0]
sage: L.zero_at(0) # Use zero_at(0) to get rid of signed zeros
[ 1.0 0.0 0.0 0.0 0.0]
[ 0.0 1.0 0.0 0.0 0.0]
[ 0.5 0.5 1.0 0.0 0.0]
[0.75 0.25 0.0 1.0 0.0]
[0.25 0.75 0.0 0.0 1.0]
sage: U.zero_at(0) # Use zero_at(0) to get rid of signed zeros
[24.0 25.0 26.0 27.0 28.0 29.0]
[ 0.0 1.0 2.0 3.0 4.0 5.0]
[ 0.0 0.0 0.0 0.0 0.0 0.0]
[ 0.0 0.0 0.0 0.0 0.0 0.0]
[ 0.0 0.0 0.0 0.0 0.0 0.0]
sage: P*A-L*U
[0.0 0.0 0.0 0.0 0.0 0.0]
[0.0 0.0 0.0 0.0 0.0 0.0]
[0.0 0.0 0.0 0.0 0.0 0.0]
[0.0 0.0 0.0 0.0 0.0 0.0]
[0.0 0.0 0.0 0.0 0.0 0.0]
sage: P.transpose()*L*U
[ 0.0 1.0 2.0 3.0 4.0 5.0]
[ 6.0 7.0 8.0 9.0 10.0 11.0]
[12.0 13.0 14.0 15.0 16.0 17.0]
[18.0 19.0 20.0 21.0 22.0 23.0]
[24.0 25.0 26.0 27.0 28.0 29.0]
Trivial cases return matrices of the right size and characteristics.
sage: A = matrix(RDF, 5, 0, entries=0)
sage: P, L, U = A.LU()
sage: P.parent()
Full MatrixSpace of 5 by 5 dense matrices over Real Double Field
sage: L.parent()
Full MatrixSpace of 5 by 5 dense matrices over Real Double Field
sage: U.parent()
Full MatrixSpace of 5 by 0 dense matrices over Real Double Field
sage: P*A-L*U
[]
The results are immutable since they are cached.
sage: P, L, U = matrix(RDF, 2, 2, range(4)).LU()
sage: L[0,0] = 0
Traceback (most recent call last):
...
ValueError: matrix is immutable; please change a copy instead (i.e., use copy(M) to change a
sage: P[0,0] = 0
Traceback (most recent call last):
...
ValueError: matrix is immutable; please change a copy instead (i.e., use copy(M) to change a
sage: U[0,0] = 0
Traceback (most recent call last):
...
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