Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
5.47068444321
sage: A.norm(1)
6.0
sage: A.norm(Infinity)
8.41421356237
sage: a = matrix([[],[],[],[]])
sage: a.norm()
0.0
sage: a.norm(Infinity) == a.norm(1)
True
nullity()
Return the (left) nullity of this matrix, which is the dimension of the (left) kernel of this matrix acting from
the right on row vectors.
EXAMPLES:
sage: M = Matrix(QQ,[[1,0,0,1],[0,1,1,0],[1,1,1,0]])
sage: M.nullity()
0
sage: M.left_nullity()
0
sage: A = M.transpose()
sage: A.nullity()
1
sage: A.left_nullity()
1
sage: M = M.change_ring(ZZ)
sage: M.nullity()
0
sage: A = M.transpose()
sage: A.nullity()
1
numerical_approx(prec=None, digits=None)
Return a numerical approximation of self as either a real or complex number with at least the requested
number of bits or digits of precision.
INPUT:
•prec - an integer: the number of bits of precision
•digits - an integer: digits of precision
OUTPUT: A matrix coerced to a real or complex field with prec bits of precision.
EXAMPLES:
sage: d = matrix([[3, 0],[0,sqrt(2)]]) ;
sage: b = matrix([[1, -1], [2, 2]]) ; e = b * d * b.inverse();e
[ 1/2*sqrt(2) + 3/2 -1/4*sqrt(2) + 3/4]
[ -sqrt(2) + 3 1/2*sqrt(2) + 3/2]
sage: e.numerical_approx(53)
[ 2.20710678118655 0.396446609406726]
[ 1.58578643762690 2.20710678118655]
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