Singular Value Decomposition

Brief introduction to Singular Value Decomposition (SVD) 1. What is SVD (Singular Value Decomposition)? 1.1 Definition Define $ \mathbf{ X } = (\vec{x_1}) $ as a $n\times m$ matrix ($n \ge m$). A fraction of $\mathbf{X}$ is: $$ \mathbf{X} = \mathbf{ U }\mathbf{ \Sigma } \mathbf{ V }^\top $$ where: $ \mathbf{U} $: $n \times n$ unitary matrix ($\mathbf{U}^* = \mathbf{U}^{-1}$) $ \mathbf{\Sigma} $: $n \times m$ rectangular diagonal matrix with non-negative real numbers on the diagonal