• rank
  • In linear algebra, the rank of a matrix A is the size of the largest collection of linearly independent columns of A (the column rank) or the size of the largest collection of linearly independent rows of A (the row rank). For every matrix, the column rank is equal to the row rank.[1] It is 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.
• linearly dependent
  • The vectors in a subset S=(v1,v2,...,vk) of a vector space V are said to be linearly dependent, if there exist a finite number of distinct vectors v1, v2, ..., vn in S and scalars a1, a2, ..., an, not all zero, such that
  • a_1 v_1 + a_2 v_2 + \cdots + a_k v_k = 0,
  • where zero denotes the zero vector.