Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
inverse()
Returns the inverse of self, without changing self.
Note that one can use the Python inverse operator to obtain the inverse as well.
EXAMPLES:
sage: m = matrix([[1,2],[3,4]])
sage: m^(-1)
[ -2 1]
[ 3/2 -1/2]
sage: m.inverse()
[ -2 1]
[ 3/2 -1/2]
sage: ~m
[ -2 1]
[ 3/2 -1/2]
sage: m = matrix([[1,2],[3,4]], sparse=True)
sage: m^(-1)
[ -2 1]
[ 3/2 -1/2]
sage: m.inverse()
[ -2 1]
[ 3/2 -1/2]
sage: ~m
[ -2 1]
[ 3/2 -1/2]
sage: m.I
[ -2 1]
[ 3/2 -1/2]
TESTS:
sage: matrix().inverse()
[]
is_bistochastic(normalized=True)
Returns True if this matrix is bistochastic.
A matrix is said to be bistochastic if both the sums of the entries of each row and the sum of the entries of
each column are equal to 1.
INPUT:
•normalized – if set to True (default), checks that the sums are equal to 1. When set to False,
checks that the row sums and column sums are all equal to some constant possibly different from 1.
EXAMPLES:
The identity matrix is clearly bistochastic:
sage: Matrix(5,5,1).is_bistochastic()
True
The same matrix, multiplied by 2, is not bistochastic anymore, though is verifies the constraints of
normalized == False:
sage: (2 * Matrix(5,5,1)).is_bistochastic()
False
sage: (2 * Matrix(5,5,1)).is_bistochastic(normalized = False)
True
184 Chapter 7. Base class for matrices, part 2