PCA and SVD explained with numpy

How exactly are principal component analysis and singular value decomposition related and how to implement using numpy. Principal component analysis (PCA) and singular value decomposition (SVD) are commonly used dimensionality reduction approaches in exploratory data analysis (EDA) and Machine Learning. They are both classical linear dimensionality reduction methods that attempt to find linear combinations of features in the original high dimensional data matrix to construct meaningful representation of the dataset. They are preferred by different fields when it comes to reducing the dimensionality: PCA are often used by biologists to analyze and visualize the source variances in datasets from population genetics, transcriptomics, proteomics and microbiome. Meanwhile, SVD, particularly its reduced version truncated SVD, is more popular in the field of natural language processing to achieve a representation of the gigantic while sparse word frequency matrices.