Does the minimum number of dependent rows in a matrix have a specific name? (the way "rank" refers to the maximum number of independent rows). This comes up in calculating distances of codes. There are plenty of algorithms to calculate rank; are there any for this minimum other than brute force? Any reference to or description of the algorithm are appreciated; same for any sw package that might have that implemented.
2026-03-31 20:53:19.1774990399
minimum number of dependent rows in a matrix
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Let $\phi: V \rightarrow W$ be a linear transformation and let $M$ be the matrix corresponding to $\phi$ using the bases $B$ and $B'$ for $V$ and $W$, respectively. In the following paper, a method for determining the dimension $d$ of the Kernel of $\phi$ is presented by looking at $M$. Their idea for determining $d$ is to count the number of linearly dependent row vectors in $M$. http://www.math.uchicago.edu/~may/VIGRE/VIGRE2008/REUPapers/Klein.pdf
Also, the following page of MATLAB Central can be helpful: http://www.mathworks.com/matlabcentral/newsreader/view_thread/157533?requestedDomain=www.mathworks.com