Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
Traceback (most recent call last):
...
ValueError: cannot add a multiple of a row to itself
sage: E = elementary_matrix(ZZ, 5, col1=3, scale=0)
Traceback (most recent call last):
...
ValueError: scale parameter of column of elementary matrix must be non-zero
AUTHOR:
•Rob Beezer (2011-03-04)
sage.matrix.constructor.identity_matrix(ring, n=0, sparse=False)
This function is available as identity_matrix(...) and matrix.identity(...).
Return the n × n identity matrix over the given ring.
The default ring is the integers.
EXAMPLES:
sage: M = identity_matrix(QQ, 2); M
[1 0]
[0 1]
sage: M.parent()
Full MatrixSpace of 2 by 2 dense matrices over Rational Field
sage: M = identity_matrix(2); M
[1 0]
[0 1]
sage: M.parent()
Full MatrixSpace of 2 by 2 dense matrices over Integer Ring
sage: M.is_mutable()
True
sage: M = identity_matrix(3, sparse=True); M
[1 0 0]
[0 1 0]
[0 0 1]
sage: M.parent()
Full MatrixSpace of 3 by 3 sparse matrices over Integer Ring
sage: M.is_mutable()
True
sage.matrix.constructor.ith_to_zero_rotation_matrix(v, i, ring=None)
This function is available as ith_to_zero_rotation_matrix(...) and matrix.ith_to_zero_rotation(...).
Return a rotation matrix that sends the i-th coordinates of the vector v to zero by doing a rotation with the (i-1)-th
coordinate.
INPUT:
•v‘ - vector
•i - integer
•ring - ring (optional, default: None) of the resulting matrix
OUTPUT:
A matrix
EXAMPLES:
36 Chapter 2. Matrix Constructor