Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
Here we make a random matrix over RR and use cmap=’hsv’ to color the matrix elements different RGB
colors (see documentation for matrix_plot for more information on cmaps):
sage: A = random_matrix(RDF, 50)
sage: plot(A, cmap=’hsv’)
Another random plot, but over GF(389):
sage: A = random_matrix(GF(389), 10)
sage: A.plot(cmap=’Oranges’)
prod_of_row_sums(cols)
Calculate the product of all row sums of a submatrix of A for a list of selected columns cols.
EXAMPLES:
sage: a = matrix(QQ, 2,2, [1,2,3,2]); a
[1 2]
[3 2]
sage: a.prod_of_row_sums([0,1])
15
Another example:
sage: a = matrix(QQ, 2,3, [1,2,3,2,5,6]); a
[1 2 3]
[2 5 6]
sage: a.prod_of_row_sums([1,2])
55
AUTHORS:
•Jaap Spies (2006-02-18)
randomize(density=1, nonzero=False, *args, **kwds)
Randomize density proportion of the entries of this matrix, leaving the rest unchanged.
Note: We actually choose at random density proportion of entries of the matrix and set them to
random elements. It’s possible that the same position can be chosen multiple times, especially for a very
small matrix.
INPUT:
•density - float (default: 1); rough measure of the proportion of nonzero entries in the random
matrix
•nonzero - Bool (default: False); whether the new entries have to be non-zero
•*args, **kwds - Remaining parameters may be passed to the random_element function of
the base ring
EXAMPLES:
We construct the zero matrix over a polynomial ring.
sage: a = matrix(QQ[’x’], 3); a
[0 0 0]
[0 0 0]
[0 0 0]
We then randomize roughly half the entries:
223