From linear algebra we know that the rank of a matrix is the maximal number of linearly independent columns or rows in a matrix. So, for a matrix, the rank can be determined by simple row reduction, determinant, etc. However, I am wondering how the concept of a rank applies to a single vector, i.e., $\mathbf{v} = [a, \ b, \ c]^{\top}$. My intuition suggests that the rank must be equal to 1, but I'm not even sure if it is defined for a vector. Can anyone help shed some light on this issue?
Thanks in advance.
