# Name for a non-square matrix with ones along the main diagonal?

Is there a name for a matrix that would be the identity matrix, except that it's not square? In other words, it has ones along the main diagonal, and zeroes off of the main diagonal. But as it's not a square matrix, it is not the identity matrix.

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I doubt there is a name... – Mariano Suárez-Alvarez May 27 '12 at 1:30
@WilliamJockusch What is the diagonal of a non-square matrix? – user38268 May 27 '12 at 1:31
I assume he means a matrix whose elements $a_{ij}$ are defined by he kronecker delta $\delta_{ij}$, but isn't necessarily square. That's the best definition I can think of. – Robert Mastragostino May 27 '12 at 2:01
@BenjaminLim: usually, the set of all entries whose row and column indices are equal. (He's talking about block matrices of the form $\begin{pmatrix} I & 0 \end{pmatrix}$ or $\begin{pmatrix} I \\ 0 \end{pmatrix}$, where $I$ is a square identity matrix and $0$ is a rectangular zero matrix of the appropriate size.) – leslie townes May 27 '12 at 2:01