Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: x,y = var(’x,y’)
sage: v = vector((x,y))
sage: vector_on_axis_rotation_matrix(v, 1)
[ y/sqrt(x^2 + y^2) -x/sqrt(x^2 + y^2)]
[ x/sqrt(x^2 + y^2) y/sqrt(x^2 + y^2)]
sage: vector_on_axis_rotation_matrix(v, 0)
[ x/sqrt(x^2 + y^2) y/sqrt(x^2 + y^2)]
[-y/sqrt(x^2 + y^2) x/sqrt(x^2 + y^2)]
sage: vector_on_axis_rotation_matrix(v, 0) * v
(x^2/sqrt(x^2 + y^2) + y^2/sqrt(x^2 + y^2), 0)
sage: vector_on_axis_rotation_matrix(v, 1) * v
(0, x^2/sqrt(x^2 + y^2) + y^2/sqrt(x^2 + y^2))
sage: v = vector((1,2,3,4))
sage: vector_on_axis_rotation_matrix(v, 0) * v
(sqrt(30), 0, 0, 0)
sage: vector_on_axis_rotation_matrix(v, 0, ring=RealField(10))
[ 0.18 0.37 0.55 0.73]
[-0.98 0.068 0.10 0.14]
[ 0.00 -0.93 0.22 0.30]
[ 0.00 0.00 -0.80 0.60]
sage: vector_on_axis_rotation_matrix(v, 0, ring=RealField(10)) * v
(5.5, 0.00098, 0.00098, 0.00)
AUTHORS:
Sebastien Labbe (April 2010)
sage.matrix.constructor.zero_matrix(ring, nrows, ncols=None, sparse=False)
This function is available as zero_matrix(...) and matrix.zero(...).
Return the nrows × ncols zero matrix over the given ring.
The default ring is the integers.
EXAMPLES:
sage: M = zero_matrix(QQ, 2); M
[0 0]
[0 0]
sage: M.parent()
Full MatrixSpace of 2 by 2 dense matrices over Rational Field
sage: M = zero_matrix(2, 3); M
[0 0 0]
[0 0 0]
sage: M.parent()
Full MatrixSpace of 2 by 3 dense matrices over Integer Ring
sage: M.is_mutable()
True
sage: M = zero_matrix(3, 1, sparse=True); M
[0]
[0]
[0]
sage: M.parent()
Full MatrixSpace of 3 by 1 sparse matrices over Integer Ring
sage: M.is_mutable()
True
58 Chapter 2. Matrix Constructor