Matrix Rank Deficiency

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns.[1][2][3] This corresponds to the maximal number of linearly independent columns of A. This, in turn, is identical to the dimension of the vector space spanned by its rows.[4] Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.