For any matrix, the following definitions hold: row rank: number of linearly independent rows column rank: number of linearly independent columns
There is a theorem stating that these 2 numbers must be the same for any matrix, and (consequently) that number is defined as the 'rank' of the matrix. For a matrix which has less columns than rows (as in your example), to say it has 'full column rank' would mean that it's rank = number of columns, and so yes, by definition all it's columns are linearly independent. I don't know if the description 'full rank' has any concrete interpretation for such matrices, though. HTH. On Monday 03 November 2003 13:32, Feng Zhang wrote: > Dear R listers, > > Just a simple question. > If we say an nxm matrix (n>m) is full rank of m, > does this mean that this matrix has linearly independent columns? > > They are the same definition or needs some proof? > > Thanks for your answer. > > Fred > > [[alternative HTML version deleted]] > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
