Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
prod_of_row_sums(cols)
Return the product of the sums of the entries in the submatrix of self with given columns.
INPUT:
•cols - a list (or set) of integers representing columns of self.
OUTPUT: an integer
EXAMPLES:
sage: a = matrix(ZZ,2,3,[1..6]); a
[1 2 3]
[4 5 6]
sage: a.prod_of_row_sums([0,2])
40
sage: (1+3)*(4+6)
40
sage: a.prod_of_row_sums(set([0,2]))
40
randomize(density=1, x=None, y=None, distribution=None, nonzero=False)
Randomize density proportion of the entries of this matrix, leaving the rest unchanged.
The parameters are the same as the ones for the integer ring’s random_element function.
If x and y are given, randomized entries of this matrix have to be between x and y and have density 1.
INPUT:
•self - a mutable matrix over ZZ
•density - a float between 0 and 1
•x, y - if not None, these are passed to the ZZ.random_element function as the upper and lower
endpoints in the uniform distribution
•distribution - would also be passed into ZZ.random_element if given
•nonzero - bool (default: False); whether the new entries are guaranteed to be zero
OUTPUT:
•None, the matrix is modified in-place
EXAMPLES:
sage: A = matrix(ZZ, 2,3, [1..6]); A
[1 2 3]
[4 5 6]
sage: A.randomize()
sage: A
[-8 2 0]
[ 0 1 -1]
sage: A.randomize(x=-30,y=30)
sage: A
[ 5 -19 24]
[ 24 23 -9]
rank()
Return the rank of this matrix.
OUTPUT:
•nonnegative integer - the rank
331