A unimodular matrix is a square integer matrix with a determinant of either +1 or -1. In other words, for a matrix \( A \) to be termed unimodular, it must satisfy the condition: \[ \text{det}(A) = \pm 1 \] Unimodular matrices have several important properties and applications, particularly in areas such as number theory, algebra, and the study of lattice structures.
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An integral square matrix is unimodular when its determinant is or . Its inverse again has integral entries, so it defines an invertible change of integer coordinates.