The purpose of this paper is to present a largely self-contained proof of the singular value decomposition (SVD), and to explore its application to the low rank approximation problem. We begin by proving background concepts used throughout the paper. We then develop the SVD by way of the polar decomposition. Finally, we show that the SVD can be used to achieve the best low rank approximation of...

Six components of sporaviridin (SVD) were successfully isolated by HPLC using methano-1 M ammonium chloride as the mobile phase. Each component possesses expectedly antimicrobial activity. To ensure the structural relationship between the intact SVD and N-acetylated sporaviridins (N-Ac-SVD), they were converted to the corresponding of N-acetates by acetylation in methanol, whose structures had ...

The authors discuss the importance of using the singular value decomposition (SVD) in computing the capacity of multiple input multiple output (MIMO) and in estimation the channel gain from the transmitter to the receiver. Examples that show how the SVD simplifies computing the MIMO channel capacity are discussed. Numerical results that show what factors determine the performance of using SVD i...

The eigenface method is a technique that has been widely used for facial recognition algorithms. The method relies on the use of a one-dimensional Singular Value Decomposition (SVD), but recently it has been argued that a two dimensional SVD would be more effective. In this study, both methods were applied to a handwritten character recognition problem. The two methods yielded similar accuracy ...