Solving matrix equation A B = C. with B(n* 1) and C(n *1)

Question

I am trying to solve a matrix equation such as A.B = C. The A is the unknown matrix and i must find it. I have B(n*1) and C(n*1), so A must be n*n.

I used the BT* A.T =C.T method (numpy.linalg.solve(B.T, C.T)). But it produces an error:

LinAlgError: Last 2 dimensions of the array must be square.

So the problem is that B isn't square.

are both `A` and `B` vectors with one column? If so, then there's no possible solution (you need more variables, specifcally you need `A` to be a square matrix). — Barranka, Sep 01 '16 at 21:35
You have two `n`-dimensional vectors and you're trying to solve for an `n`-by-`n` matrix? Unless `n` is 1 or `A` is the zero vector, that's underspecified and there are infinitely many correct answers. — Tanner Swett, Sep 01 '16 at 21:37
Sorry, i changed the question to be more correct.@Barranka @Tanner Swett — Rabih Assaf, Sep 02 '16 at 11:03
The "problem" is that your equation has infinitely many solutions. Do you just want an arbitrary solution or do you need a *good* solution? What are you trying to accomplish by solving this equation? — Tanner Swett, Sep 02 '16 at 13:33

score 0 · Answer 1 · answered Sep 01 '16 at 21:34

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Here's a little example for you:

import numpy as np

a = np.array([[1, 2], [3, 4]])
b = np.array([5, 6])
x = np.linalg.solve(a, b)

print "A={0}".format(a)
print "B={0}".format(b)
print "x={0}".format(x)

For more information, please read the docs

answered Sep 01 '16 at 21:34

BPL

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the problem that a isn't square – Rabih Assaf Sep 02 '16 at 10:53
This solves for one of the vectors. OP asked how to solve for the matrix (which doesn't seem very useful but that was the question). – interjay Sep 02 '16 at 11:10
@interjay OP edited the question changing the meaning... this one was a good one few hours ago – BPL Sep 02 '16 at 11:11
OP changed the variable names, but the question still specified that the input is two vectors and the output is a matrix. – interjay Sep 02 '16 at 11:18
@interjay I see, well, then I misunderstood the question – BPL Sep 02 '16 at 11:26

score 0 · Answer 2 · answered Sep 02 '16 at 11:01

If you're solving for the matrix, there is an infinite number of solutions (assuming that B is nonzero). Here's one of the possible solutions:

Choose an nonzero element of B, Bi. Now construct a matrix A such that the ith column is C / Bi, and the other columns are zero.

It should be easy to verify that multiplying this matrix by B gives C.

Solving matrix equation A B = C. with B(n* 1) and C(n *1)

2 Answers2