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I have two matrices of equal dimensions $(m \times n)$. If it helps, one matrix is the raw data, while the other is transformed.

I've plotted PC1 vs PC2 for both datasets individually, but then I realized I couldn't compare directly because the principal components likely change between the two matrices.

So is there a way, in R, that I can plot matrix2 using PC1 and PC2 from matrix1?

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    $\begingroup$ As long as the dimensions are consistent, you can. This becomes a linear algebra question. If you make it an "R" question, then folks here will get truculent. $\endgroup$ – EngrStudent Feb 10 '17 at 17:45
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The prcomp function in R has a handy predict method:

set.seed(42)
a <- matrix(rnorm(1000), ncol=10)
b <- matrix(rnorm(1000), ncol=10)

model <- prcomp(a, center=T, scale=T)
b_pca <- predict(model, b)
plot(b_pca[,1:2])
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