The problem of matrix decomposition, also known as matrix factorization problem, is widely investigated in data mining community. Especially Boolean case, where entries of matrices are 0s and 1s. In this thesis we explore the extension of matrix decomposition problem for ordinal data, i.e. data where attributes are values from ordered scales. The replacement of the two-element set of Boolean values and Boolean operations by a multiple-valued set of grades and multiple-valued operations introduced various non-trivial problems. We examine existing algorithms for ordinal data and propose three new algorithms for matrix decomposition problem. We demonstrate that the proposed algorithms deliver decompositions with informative and easy-to-understand factors by analysing real datasets. Moreover, we also compare algorithms presented on synthetic datasets.