Calculating Mean Square Error with Pseudo Inverse Approach

[nikki92]

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?

 

[LCKurtz]

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.

 

[nikki92]

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 .

 

[D H]

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.