I have study on entity embedding, and there is a formula that can projection the vector $h$ on a specific hyperplane.
$$\mathbf {h}_{\perp} =\mathbf {h}-\mathbf {w}_r^\top \mathbf {h}\mathbf {w}_r$$
The approach to calculating projection vector is origin vector subtract the vector projection on the normal vector of the hyperplane.
But, what's the meaning of $\mathbf {w}_r^\top \mathbf {h}\mathbf {w}_r$? I found a lot of question use this formula, but I can't find an example to show the use of this formula.
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2026-03-26 06:31:00.1774506660
What's the meaning of $\mathbf {w}_r^\top \mathbf {h}\mathbf {w}_r$ in vector projection
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$\mathbf{w}_r^T\mathbf{h}$ is the scalar product between vectors $\mathbf{w}_r$ and $\mathbf{h}$. Then you multiply $\mathbf{w}_r$ by this scalar to get a vector $\mathbf{w}_r^T\mathbf{h}\mathbf{w}_r$ which you subtract from $\mathbf{h}$ to get $\mathbf{h}_\perp$.
To apply this formula, you want $\mathbf{w}_r$ to be a unit vector orthogonal to the (hyper)plane you are projecting onto.