The singular value decomposition of a matrix is used to derive systematically the Moore-Penrose inverse for a matrix bordered by a row and a column, in addition to the Moore-Penrose inverse for the ...

Principal component analysis (PCA) is a classical machine learning technique. The goal of PCA is to transform a dataset into one with fewer columns. This is called dimensionality reduction. The ...

We present deviation inequalities of random operators of the form $N^{-1}\sum_{i=1}^{N}X_{i}\otimes X_{i}$ from the average operator ${\Bbb E}(X\otimes X)$, where $X ...