Mathematical definition of the SVD Let X denote an mx n matrix of real-valued data and rank r,where without loss of generality mn, and therefore r≤n. is the element value of the ith row in the jth column. The equation for singular value decomposition of X is the following: X=USVT (5.1)Mathematical definition of the SVD Let X denote an m × n matrix of real-valued data and rank r, where without loss of generality m ≥ n, and therefore r ≤ n. xij is the element value of the ith row in the jth column. The equation for singular value decomposition of X is the following: (5.1)