Solving the linear equation

Hi,

For a simple explanation, an example is 21 = m x 7. m = 21/7 = 3. If I use the m I obtained to time 7, it should be equal to 21.

But above is just numbers, not matrix.

For solving similar problem on matrix, I would like to do a linear conversion from one matrix (P) to another (T).

My equation is T = MP, while T and P are both 3 by 24 matrices. I need to work out M.

My understanding is that M = T/P and M is a 3 x 3 matrix.

But why after I obtained M, I use M*P, it doesn't equal to T anymore. Why is that?

[Ranjan Sonalkar]

I would reframe the equation as y = Ax, where y contains the 9 terms of T, x contains the 9 unknowns from M and A would be the reformatted T. Then it is a least-squares solution.

Answer 1

[Matt J]

Because you have 72 equations and only 9 unknowns. The system is over-determined.

Answer 2

[Torsten]

M = T*P.'*inv(P*P.')

is the least-squares solution.

But you cannot expect that T=M*P is exactly satisfied.