The Quattro Sensor and Luma

Started Jul 18, 2014 | Discussions thread
JimKasson
JimKasson Forum Pro • Posts: 45,354
Re: Use Octave or Matlab

Joofa wrote:

Hi, sure, my pleasure.

An equation of the form, Y = a*T + b*M + c*L, can be written as:

Y = Ax, where matrix A = [T M L] and vector x = [a b c]'

Now we need to solve for x = [a b c]'. In general we can't use x = A^-1*Y, because A is not invertible (usually it is not square). If we have more measurements than the number of components of vector x, (which in this case is 3 because x = [a b c]'), then it is an overdetermined situation. In this case there exists a single global min. solution. And, to get that is as mentioned below.

Ax = Y

Multiply both sides by A' to get:

A'Ax = A'Y

now (A'A) is usually invertible. So we get:

x = (A'A)^-1*A'*Y.

The good thing about this is that even in those rare cases when A is invertible then it will yield the regular solution, which is x = A^-1 * Y, because:

x = (A'A)^-1*A'*Y,

= A^-1 * (A')^-1 * A' * Y, now [(A')^-1*A' = Identitiy],

= A^-1 * Y.

Got it. But if you asked me to explain it to you tomorrow, I'm sure I'd draw a blank.

Thank you.

Jim

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