Doing PCA on a matrix using SVD yields a result of three matrices, expressed as:
$$ M = U \Sigma V^T $$
where $M$ is our initial data with zero mean.
If we want to make a plot of the two principle components we project the data onto principal component space.
$$ Z = M * V $$
and then use the two first columns of Z for our plot. Maybe I have already answered my own question, but I am struggling to understand if $Z$ is what would be called the Principle Component matrix, and if not, how do we find that?
Also, I am not sure what the operation $M*V$ does to the data. As I understand it, $V$ is an expression of the general trends of each of the attributes in the data set. By calculating the dot product between our data $M$ and the trends $V$ of the data, we end up with a matrix (PC matrix?) that captures the original data in a structured manner which allows for dimensionality reduction.
Are my assumptions correct, or have I misread the theory?