I know a square matrix is called orthogonal if its rows (and columns) are pairwise orthonormal
But is there a deeper reason for this, or is it only an historical reason? I find it is very confusing and the term would let me assume, that a matrix is called orthogonal if its rows (and columns) are orthogonal and that it is called orthonormal if its rows (and columns) are orthonormal but apparently that's not conventional.
I know that square matrices with orthogonal columns have no special interest, but thats not the point. If I read the term orthogonal matrix my first assumption is, that its rows (and columns) are orthogonal what is correct of course, but the more important property is that they are also orthonormal
So, Question: Why do you call an orthogonal matrix orthogonal and not orthonormal? Wouldn't this be more precisely and clearly?