Question: Consider a data matrix A Rmn and observation matrix Y Rmd. Recall that the (ordinary) matrix least squares problem AX Y can be seen as

Consider a data matrix A Rmn and observation matrix Y Rmd. Recall that the (ordinary) matrix least squares problem AX Y can be seen as projecting the (columns of) Y onto the range of Ai.e., AX = AAY where AA is a projection matrix. In this setting, our model AX Y is such that we are modeling errors in our measurementsthat is

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