Given $X\in\mathbb{R}^{T \times N}$, I would like to know how to find $W\in\mathbb{R}^{T \times N}$ such that $X'X=W'W-\frac{1}{T}W'\iota_T\iota_T'W$. $\iota_T$ denotes the vector of ones of length T. The term $\frac{1}{T}W'\iota_T\iota_T'W$ can also be written as the Matrix $\hat{\mu}\hat{\mu}'$ where $\hat{\mu}$ is the sample mean of $W$. Given $X$ does not have sample mean $0$, how can I solve this problem?
2026-04-02 14:12:59.1775139179
Find $W\in\mathbb{R}^{T \times N}$ such that for $X\in\mathbb{R}^{T \times N}$: $X'X=W'W-\frac{1}{T}W'\iota_T\iota_T'W$
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