Fair to say there are "twice" as many square matrices as rectangular? Is it fair to say that there are at least twice as many square matrices as there are rectangular? I was thinking something like this.... Let R be a rectangular matrix with m rows and n columns, and suppose either m < n or m > n. Then, we can associate two square matrices with R, namely RRt, and RtR, with Rt being R Transpose. In other words, for every rectangular matrix there can be associated (at least) two square matrices. Google brought up nothing, so I figured I would ask it here. It's not for homework or anything; just out of interest.