I wish to find out Moore Penrose psudo inverse of a matrix with variable row $4 \times k$ matrix with $k \in \mathbb{N}$ with entries a function of k. Is it possible to write down in SAGE?
Unless I'm misunderstanding your question (which is a bit ambiguous what does mean "with entries a function of k" ?), this should do :
sage: def myfunc(k): return floor(k*random())
sage: def make_4xk_matrix(k):
....: return matrix(ZZ,[[myfunc(k) for t in (1..k)] for l in (1..4)])
....:
sage: make_4xk_matrix(6)
[1 5 3 3 4 3]
[5 2 3 3 2 3]
[2 3 1 3 3 3]
[0 2 3 2 1 5]
Note that the entries belong to $\mathbb{Z}$ : $\mathbb{N}$ is not a ring and Sage's matrix refuses it.
Then,
sage: L = [0, 4, 4, 1, 5, 1, 3, 1, 3, 2, 2, 1, 0, 5, 3, 3, 3, 2, 3, 3, 1, 0, 5, 2]
sage: M = matrix(4, L)
sage: M
[0 4 4 1 5 1]
[3 1 3 2 2 1]
[0 5 3 3 3 2]
[3 3 1 0 5 2]
sage: M.pseudoinverse()
[-15573/108749 18903/108749 -3411/108749 12744/108749]
[ -7882/108749 -13917/108749 19684/108749 6513/108749]
[ 22998/108749 18697/108749 -11848/108749 -19721/108749]
[-15071/108749 11925/108749 19094/108749 -7925/108749]
[ 15869/108749 -5687/108749 -12781/108749 10163/108749]
[-15989/108749 -2610/108749 13467/108749 9942/108749]
Asked: 2018-01-20 07:52:53 +0100
Seen: 600 times
Last updated: Jan 20 '18
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