The paper deals with the process of gradual acceptance of the matrix theory by mathematical community. This process began in the second part of the 19th century and continued till the second part of the 20th century.

Until then, a majority of mathematicians formulated their results, which are presently well-incorporated in the matrix theory, in terms of determinants, bilinear and quadratic forms. The process resulted in new ways of expressing these results, requiring new terminology, new symbolism.