Pseudo Inverse Matrix
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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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Answers (3)
Walter Roberson
on 11 Jan 2012
Those systems are not possible. Matrix multiplication of a 4x3 with a 3x4 will give you a 4x4 not a 3x3 .
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Davide
on 12 Jan 2012
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Walter Roberson
on 12 Jan 2012
? Are you looking for the mathematical definition of pseudo-inverse? Or are you looking for it worked-out symbolically in the 4x3 case?
Dr. Seis
on 12 Jan 2012
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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