Calculate the original matrix from the centered matrix without the mean of the original matrix?

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Janak Trivedi

H. Satori

No, it is not possible to calculate the original matrix from a centered matrix without the mean of the original matrix. The mean of the original matrix is an essential piece of information needed to reverse the centering operation and recover the original matrix. The centering operation involves subtracting the mean of each column or row from the corresponding elements, so without the mean, the information needed to reverse the operation is lost.

Rut Su

Hi H. Satori

Reconstructing the original matrix from a centered matrix requires knowledge of the mean of the original matrix, which, if unavailable, makes it mathematically impossible to revert the centering process.

Hi Janak, Hi Su,

Thank you for your answer to my question.

but, mathematically it's possible for the 3 by 3 matrix because of a limited number of unknown variables.

the challenge is for higher matrices.

what about the use of an approximation of the mean? maybe for educational purposes.

Hassan