Non-square matrix inverse

I have a set of data, where x is a 8*100 matrix. I convert it into xyz coordinates by multiplying with a transformation vector t (3*8), so that:

B = t*x, resulting in B which is a 3*100 matrix.

I am trying to figure out a way to go from B back to x.

I have tried to do x = pinv(t) * B, but the values were significantly off.

Would appreciate any help!

[Matt J]

I have tried to do x = pinv(t) * B, but the values were significantly off.

That's the best you are going to be able to do.

Answer 1

[John D'Errico]

You CANNOT do so. That is, you cannot learn the original values. You cannot go backwards. A simple example is:

Choose any two numbers. Call them x and y. I'll pick them for you as an example:

x = rand

x = 0.6625

y = rand

y = 0.2189

Having done so, add them together.

z = x + y

z = 0.8814

Now, knowing ONLY the value of z, and the fact that you added x and y together to get z, can you now infer the original values of x and y? OF COURSE NOT!

x and y could be ANY numbers that added together, yield 0.8814.