from __future__ import division, print_function   # Python 3
from sympy import init_printing
init_printing(use_latex='mathjax',use_unicode=False)  # Affichage des résultats

from sympy import Matrix

Matrix([[2, 5, 6], [4, 7, 10], [1, 0, 3]])

Matrix(2, 3, [1, 2, 3, 4, 5, 6])

Matrix([1,2,3,4])

M = Matrix([[5, 2], [-1, 7]])
N = Matrix([[0, 4], [0, 5]])
M + N

M * N

4 * M

M ** 5

M**-1

N**-1

from sympy import I
M = Matrix(( (1,2+I,5), (3,4,0) ))
M

M.transpose()

from sympy import I
M = Matrix(( (1,2+I,5), (3,4,0) ))
M

M[0,1]

M[1,1]

M.row(1)

M.col(0)

from sympy import ones,zeros
ones(2)

zeros((2, 4))

from sympy import eye
eye(3)

from sympy import diag
diag(1,2,3)

diag(1, 2, Matrix([[7,8],[2,3]]))

M = Matrix([[1, 2, 0, 3], [2, 6, 5, 1], [-1, -4, -5, 2]])
M.rref()

M = Matrix([[1, 2, 0, 3], [2, 6, 5, 1], [-1, -4, -5, 2]])
M.nullspace()

M = Matrix([[2, 5, 6], [4, 7, 10], [1, 0, 3]])
M.det()

M = Matrix([[3, -2,  4, -2], [5,  3, -3, -2], [5, -2,  2, -2], [5, -2, -3,  3]])
from sympy.abc import x
M.charpoly(x)

M.charpoly(x).as_expr()

from sympy import factor
factor(_)

 M

w = Matrix((1,2,3,4))
v = Matrix((1,1,1,0))
w

v

M * w

M * v

5 * v

M.eigenvals()

M.eigenvects()