# A is not square but rank(A) = rank(A') ???

by mikeph
Tags: ranka, square
 P: 1,171 Hi Can anyone help with understand a basic idea, I have a matrix A in MATLAB which is 100x3000. I have checked and there exist many columns of A that are all zeros. But apparently rank(A) = rank(A') = 100 Wikipedia states that the rank of an m x n matrix cannot be higher than m nor n... my interpretation of this sentence is that rank(A) ≤ min(m, n), is that correct? If so, surely that means my matrix is full-rank despite having zero columns? My understanding is that a full-rank matrix has fully orthogonal rows/columns, and since my matrix A clearly has multiple columns filled with only zeros, it cannot possibly be full-rank. So why is rank(A) = 100? Can someone tell me my interpretation of wikipedia is wrong and that this matrix is indeed really rank-deficient, it would make my day. Thanks edit- bonus question... the nullspace of A is 3000x2900. So surely that would confirm the idea that there are only 100 linearly independent rows/columns in A?
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