Calculating Mean Square Error with Pseudo Inverse Approach

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Homework Help Overview

The discussion revolves around calculating the mean square error using the pseudo inverse approach in the context of linear algebra. Participants are working with a 11x9 matrix A, a 11x1 vector F, and a 11x11 diagonal matrix R, exploring the implications of these dimensions on the resulting calculations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to derive the mean square error and are questioning the dimensionality of the resulting matrices. There is confusion regarding the expected dimensions of the output vector F and the interpretation of the equation AF=R.

Discussion Status

Some participants have provided affirmations regarding the calculations, while others express confusion about the dimensionality of the matrices involved. There is an ongoing exploration of how to derive the optimal vector F, with no clear consensus reached on the correct approach.

Contextual Notes

Participants are grappling with the implications of working with an overdetermined system and the definitions of matrix multiplication in this context. The dimensionality of the matrices is a central point of confusion, particularly regarding the product of A and F.

nikki92
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Find the mean square error using the pseudo inverse approach.

I am given a 11X9 matrix A, a 11X1 vector F and R = 11X11 diagonal matrix

so Rhat = A[(A'A)^-1 ]A' R . Then I get a 11X11 matrix. Shouldn't I get getting a 8X11 matrix How do I get the most optimum vector F?
 
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nikki92 said:
Find the mean square error using the pseudo inverse approach.

I am given a 11X9 matrix A, a 11X1 vector F and R = 11X11 diagonal matrix

so Rhat = A[(A'A)^-1 ]A' R . Then I get a 11X11 matrix.

Correct.

Shouldn't I get getting a 8X11 matrix?

No.

How do I get the most optimum vector F?

I don't know.
 
I have a linear question A*F =R where R is the diagonal 11 x 11 matrix A is 9X11 and F is 9X1. This system is over determined. I am confused on how to get the values of F .

I get that F =[(A'A)^-1 ]A' R which gives me a 9 x 11 matrix which does not make sense .
 
nikki92 said:
I have a linear question A*F =R where R is the diagonal 11 x 11 matrix A is 9X11 and F is 9X1. This system is over determined. I am confused on how to get the values of F .

I get that F =[(A'A)^-1 ]A' R which gives me a 9 x 11 matrix which does not make sense .
Your equation AF=R is not overdetermined. It doesn't even make sense. There is no such thing as the product of a 9x11 matrix with a 9x1 matrix. If your A was 11x9, then the product AF would be defined, but it's dimensionality would be 11x1, not 11x11.
 

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