Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: M = M.change_ring(ZZ)
sage: M.nullity()
0
sage: A = M.transpose()
sage: A.nullity()
1
matrix_window(row=0, col=0, nrows=-1, ncols=-1, check=1)
Return the requested matrix window.
EXAMPLES:
sage: A = matrix(QQ, 3, range(9))
sage: A.matrix_window(1,1, 2, 1)
Matrix window of size 2 x 1 at (1,1):
[0 1 2]
[3 4 5]
[6 7 8]
We test the optional check flag.
sage: matrix([1]).matrix_window(0,1,1,1, check=False)
Matrix window of size 1 x 1 at (0,1):
[1]
sage: matrix([1]).matrix_window(0,1,1,1)
Traceback (most recent call last):
...
IndexError: matrix window index out of range
Another test of bounds checking:
sage: matrix([1]).matrix_window(1,1,1,1)
Traceback (most recent call last):
...
IndexError: matrix window index out of range
maxspin(v)
Computes the largest integer n such that the list of vectors S = [v, v∗A, ..., v∗A n ] are linearly independent,
and returns that list.
INPUT:
•self - Matrix
•v - Vector
OUTPUT:
•list - list of Vectors
ALGORITHM: The current implementation just adds vectors to a vector space until the dimension doesn’t
grow. This could be optimized by directly using matrices and doing an efficient Echelon form. Also, when
the base is Q, maybe we could simultaneously keep track of what is going on in the reduction modulo p,
which might make things much faster.
EXAMPLES:
sage: t = matrix(QQ, 3, range(9)); t
[0 1 2]
[3 4 5]
[6 7 8]
sage: v = (QQ^3).0
213