Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: (~M * M).simplify_rational()
[1 0 0]
[0 1 0]
[0 0 1]
sage: matrix(SR, 1, 1, 1).inverse()
[1]
sage: matrix(SR, 0, 0).inverse()
[]
sage: matrix(SR, 3, 0).inverse()
Traceback (most recent call last):
...
ArithmeticError: self must be a square matrix
Transposition:
sage: m = matrix(SR, 2, [sqrt(2), -1, pi, e^2])
sage: m.transpose()
[sqrt(2) pi]
[ -1 e^2]
.T is a convenient shortcut for the transpose:
sage: m.T
[sqrt(2) pi]
[ -1 e^2]
Test pickling:
sage: m = matrix(SR, 2, [sqrt(2), 3, pi, e]); m
[sqrt(2) 3]
[ pi e]
sage: TestSuite(m).run()
Comparison:
sage: m = matrix(SR, 2, [sqrt(2), 3, pi, e])
sage: cmp(m,m)
0
sage: cmp(m,3) != 0
True
sage: m = matrix(SR,2,[1..4]); n = m^2
sage: (exp(m+n) - exp(m)*exp(n)).simplify_rational() == 0
True
# indirect test
Determinant:
sage: M = matrix(SR, 2, 2, [x,2,3,4])
sage: M.determinant()
4*x - 6
sage: M = matrix(SR, 3,3,range(9))
sage: M.det()
0
sage: t = var(’t’)
sage: M = matrix(SR, 2, 2, [cos(t), sin(t), -sin(t), cos(t)])
sage: M.det()
cos(t)^2 + sin(t)^2
Permanents:
304 Chapter 16. Symbolic matrices