ruutmaatriksil

Ruutmaatriksil is an Estonian phrase used in mathematical writing to indicate that a statement concerns a square matrix. It is the inessive singular form of the compound noun ruutmaatriks, built from ruut (square) and maatriks (matrix). The expression is common in educational texts, theoretical articles, and problem solutions to specify the domain of a given property or operation.

In practice, ruutmaatriksil is used to name the matrix that the statement refers to, typically with a capital letter such as A or B. For example, mathematical assertions about determinants, inverses, eigenvalues, ranks, or traces are often introduced with the clause that applies “on a square matrix” such as Ruutmaatriksil A. This distinguishes properties that hold for square matrices from those that may apply to rectangular matrices.

Grammatically, -il marks the inessive case, indicating location or context: the property is stated on the square matrix itself. The construction is part of a broader Estonian mathematical terminology that names the subject of discussion directly in the sentence, aligning with the common English practice of saying “for a square matrix A.”

See also ruutmaatriks, determinant, eigenvalue, inverse, and Estonian mathematical terminology. The phrase Ruutmaatriksil functions as a concise contextual marker that helps readers immediately identify the scope of a theorem or example.