detA1k1k

detA1k1k is not a standard term in mainstream mathematical nomenclature. In practice, it usually refers to the determinant of a matrix that is labeled A1k1k in a specific source or context. The concatenation A1k1k could denote a matrix named by those indices, or a matrix with subscripts that are written together, depending on the author’s notation. Because notational conventions vary, the exact meaning of detA1k1k is context-dependent and should be clarified where it appears.

The determinant det(A) is defined for square matrices A and yields a scalar that encodes properties such as invertibility and volume scaling of the associated linear transformation. When encountering detA1k1k, one must identify the corresponding matrix A1k1k and ensure it is square before applying the determinant operation. If A1k1k is a smaller 2x2 matrix with entries a, b, c, d, then detA1k1k equals ad − bc. For larger matrices, the determinant is computed via standard methods (expansion, row-reduction, or LU decomposition) and retains the same interpretation as the determinant of any square matrix.

Zero determinants indicate singular matrices with nontrivial null spaces. The determinant also satisfies multiplicativity det(AB) = det(A) det(B) for square matrices A and B, and changes sign under a row swap.

Because detA1k1k is not a universal notation, readers should consult the source in which the term appears to determine the exact matrix A1k1k and the intended interpretation of the determinant. See also det, determinant, and matrix notation.