there is absolutely no sense in which the SVD/PCA decomposition is just a rotation matrix. you should probably review your linear algebra textbook (hint: scaling is extremely important).
PCA is an orthogonal transformation of the covariance matrix, so like all orthogonal transformations, it’s _literally a rotation_ in N-dimensional space.
SVD is more complex but ultimately it’s just another useful decomposition of a matrix.
I’m not sure why you’re both negative and dismissive. Transformation matrices in graphics are a good and approachable way to get used to linear transformations, which turn out to be useful pretty much everywhere.
Whether or not that helps you with ML depends more on what you’re doing in ML. FAANG doesn’t have a monopoly on ML or on interesting work in ML.
Your fixation on the rotation matrix == 3D graphics is not right
SVD, and PCA are also examples.
there is absolutely no sense in which the SVD/PCA decomposition is just a rotation matrix. you should probably review your linear algebra textbook (hint: scaling is extremely important).
Cognoboffin is exactly right. SVD decomposed matrix into a sequence of rotation, scaling and unrotation matrices.
If anyone needs a review it's not cognoboffin.
You led with the claim you have never seen a rotation matrix in ML. I am having doubts about whether you have the ability to recognise one.
I suspect new hires get a free pass as long as they can talk a storm about backpropagation these days.
PCA is an orthogonal transformation of the covariance matrix, so like all orthogonal transformations, it’s _literally a rotation_ in N-dimensional space.
SVD is more complex but ultimately it’s just another useful decomposition of a matrix.
I’m not sure why you’re both negative and dismissive. Transformation matrices in graphics are a good and approachable way to get used to linear transformations, which turn out to be useful pretty much everywhere.
Whether or not that helps you with ML depends more on what you’re doing in ML. FAANG doesn’t have a monopoly on ML or on interesting work in ML.
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SVD is the decomposition of a matrix into two rotation matrices and a scaling matrix, by definition:
https://en.wikipedia.org/wiki/Singular_value_decomposition
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