Singular value decomposition (SVD) is an important matrix decomposition in numerical linear algebra. Its theoretical importance comes from its ability to decompose a matrix into simpler matrices that better describes the transformations geometric properties. The generality of this decomposition makes it an all-purpose tool that is used in many areas of the mathematical sciences. Some applications of singular value decomposition include image compression, linear regression, and rank approximation of a matrix.

A standard technique in matrix approximation is the truncated singular value decomposition (TSVD). This technique gives a good approximation while minimizing the amount of data needed to store. My project focused on a slightly different method for approximating a matrix, known as singular value hard thresholding (SVHT). My presentation will focus on background theory of the SVD, TSVD, and SVHT, as well as applications.