1detB

1detB is not a standard or widely used mathematical term, and its meaning can vary by source. In practice, when this notation appears, it is typically encountered in contexts involving block matrices or typographical variants, rather than as a universally defined operator.

Possible interpretations include:

- Detailing a 1x1 block: in a partitioned or block matrix B, some authors may use 1detB to denote the determinant of the specific 1×1 block on a diagonal or in a given position. In that case, 1detB would simply equal the scalar value of that single entry.

- Distinguishing a minor or subdeterminant: in certain treatments of minors or block determinants, 1detB might be used informally to refer to the determinant of a particular 1×1 submatrix, though this usage is not standardized.

- A typographical variant: 1detB could be a misprint or shorthand for det(B) or det(Bij) in texts that label blocks or indices with numbers.

Examples:

- If B is a block-diagonal matrix with a 1×1 block [a] and other blocks, some authors might denote the determinant of that block as 1detB, which would equal a.

- If B = [b] is a 1×1 matrix, its determinant is det(B) = b; whether one writes 1detB depends on the source, but the value remains b.

Notes:

Because 1detB is not standardized, it is important to consult the specific source for its definition. In formal writing, it is generally preferable to use det(B) for determinants and det(Bij) or det(B11) for determinants of particular submatrices or blocks. See also: determinant, block matrix, principal minor.