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4 space indentation, please.

> Currently there are two suggestions for interfaces: Either the standard fit interface or rotatefactors which is more similar to Matlabs interface. I am not a big fan of the...

The `rotate` interface usage, you presented is good. Just one thing I'd like you to change. Please, provide latinised parameters for rotation constructors instead of Unicode symbols. Using Unicode for...

Yep, the compact output would be a nice thing. Meanwhile, try to use `;` at the end of the expression to suppress output.

> It could make sense to print the command that allows printing all results, as it's not easy to find. Good idea, will do.

> For the layout problem raised in the issue, I would suggest [Term's Tables](https://fedeclaudi.github.io/Term.jl/dev/ren/table/) for styled terminal output. The table layout and handling comes from `StatsBase.CoefTable`, so the work needs...

`transform` is deprecated. Please, use `predict` instead. See the updated example here: https://juliastats.org/MultivariateStats.jl/dev/pca/#Example

Please, update. A new version has been published.

> Might be nice to have an abstract dimensionality reduction type in there that linear, nonlinear, and latent variable types can subtype. That would be `AbstractDimensionalityReduction`

Loadings are scaled eigenvectors. It will be easy to add them to every eigendecomposition-based method.