# What is the term for a matrix whose columns are orthogonal?

What is the term for a matrix whose columns are mutually orthogonal, but not necessarily othonormal?

I can't name such a matrix "orthogonal" because that would imply that all columns are unit vectors. By the way, why don't we name these matrices "orthonormal" instead of "orthogonal"? But that fight is over, I guess.

In other words, what is the term for a matrix $A$ for which $A^TA$ is a diagonal matrix, but not necessarily $I$?

One famous example are Hadamard matrices. I'd like to have a shorter term than "matrix whose rows are mutually orthogonal".

For my purpose it would be sufficient to have such a term for square matrices, but I'm also interested in a more general term that also covers non-square matrices.

• I guess you've seen this discussion Feb 13, 2017 at 12:38
• So it is a matrix of the forma $OD$, with $D$ diagonal and $O$ orthogonal --in the need of a better name you may name it an "OD matrix", which at least is short and self-explanatory Feb 13, 2017 at 12:56
• @PietroMajer This would be a great answer, no need to hide it in the comments.
– vog
Feb 14, 2017 at 19:10

Since it is a matrix of the form $OD$, with $D$ diagonal and $O$ orthogonal, in the need of a better term you may name it an "OD matrix", which at least is short and self-explanatory.
Rmk: Curiously, OD matrices already exist, in Transportation Planning, where $OD$ stands for "Origin\Destination."