Pseudo Inverse Matrix

Hi everybody, I have a question about pseudo-inverse matrix and solve the equation with that matrix inside. I need to solve this system:

H1j = H1 Hj+ with dimension (3x3) = (4x3) (3x4) and

Hj1 = Hj H1+ with dimension (3x3) = (4x3) (3x4)

(where 1j, 1 are the indices and j+ means j as indices and + as pseudo inverse matrix) (I hope that you'll understand) so in the two equation I know everything but not: Hj+ and Hj

Can someone help me? Of course you can ask me some explanation...

Answer 1

[Walter Roberson]

Those systems are not possible. Matrix multiplication of a 4x3 with a 3x4 will give you a 4x4 not a 3x3 .

Answer 2

[Davide]

Ok, but anyway I'm looking for some kind of mathematics relationship between the Hj and its pseudo inverse Hj+. For sure should be some connection between them, I need for example for all the component of one matrix the dependence in the other matrix:

h1 = F(h1+) or h2=F(h2+) .........

F is the unknown Function.

Thanks for your help.

[Walter Roberson]

? Are you looking for the mathematical definition of pseudo-inverse? Or are you looking for it worked-out symbolically in the 4x3 case?

Answer 3

[Dr. Seis]

If you have the following situation:

G*m = d

where,

G = (MxN) % Known
m = (NxP) % Unknown
d = (MxP) % Known

Then to find m, you can either do:

m = G\m

Or... the not recommended method (from an execution time and numerical accuracy standpoint) which involves computing the pseudoinverse or generalized inverse of G, which is done by:

generalize_inverse_of_G = (G'*G)\G'

and

m = generalize_inverse_of_G * d