Pseudo Inverse Matrix

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Davide
Davide 2012-1-11
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...

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回答（3 个）

Walter Roberson
Walter Roberson 2012-1-11
Those systems are not possible. Matrix multiplication of a 4x3 with a 3x4 will give you a 4x4 not a 3x3 .
Davide
Davide 2012-1-12
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.
  1 个评论
Walter Roberson
Walter Roberson 2012-1-12
? Are you looking for the mathematical definition of pseudo-inverse? Or are you looking for it worked-out symbolically in the 4x3 case?

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Dr. Seis
Dr. Seis 2012-1-12
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

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