singular value decomposition the process of singular value decompositionalso known as svdis another matrix decomposition or factorization process such that we are able to break down matrix to obtain singular vectors and singular values any real matrix will always be decomposed by svd even if eigen decomposition may not be applicable in some cases mathematicallysvd can be defined as follows considering matrix having dimensions such that denotes total rows and denotes total columnsthe svd of the matrix can be represented with the following equation ' ' sm' vnt' this gives us the following main components of the decomposition equation um is an unitary matrix where each column represents left singular vector sm is an matrix with positive numbers on the diagonalwhich can also be represented as vector of the singular values vtn is an unitary matrix where each row represents right singular vector in some representationsthe rows and columns might be interchanged but the end result should be the samei and are always orthogonal the following snippet shows simple svd decomposition in python in [ ]svd np array([[ ][ ][ ]]usvt np linalg svd(mprint('getting svd outputs:-\ 'print(' :\ ' '\ 'print(' :\ ' '\ 'print('vt:\ 'vt'\ 'getting svd outputs: [ - - - ] vt[ [- - [- ]svd as technique and the singular values in particular are very useful in summarization based algorithms and various other methods like dimensionality reduction