How to solve a Non-Square Matrix Equation?

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SUMMARY

The discussion focuses on solving the equation A = BxC, where Matrix A has dimensions [7000, 1], Matrix B is unknown with dimensions [7000, 8], and Matrix C has dimensions [8, 1]. Due to Matrix C being non-square, its inverse cannot be calculated, leading to an underdetermined system with more unknowns than equations. The recommended approach to find a solution is to utilize the 'minimum norm' solution method, which is applicable when solutions exist.

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Homework Statement



I have to solve an equation like this:

Matrix A: dimensions [7000, 1]
Matrix B: dimensions [7000,8]
Matrix C: dimensions [8,1]

Matrix B is unknown.

Homework Equations



A=BxC

The Attempt at a Solution



I can't calculate the inverse of Matrix C because it is not square, then I don't know how to isolate B...
 
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You have what is referred to as an 'underdetermined system' where there are more unknowns (8 x 7000 = 56000) than there are equations (i.e. 7000). In this situation there are either no solutions or an infinite number of solutions. If you are being asked to find 'any' solution, one common (though arbitrary) method is to find what is called the 'minimum norm' solution (assuming solutions exist).
 

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