trasponibile

Trasponibile is an Italian adjective meaning capable of being transposed. In mathematics, the term is used to describe objects for which the transpose operation can be applied, most notably matrices. The transpose of a matrix A = [aij] is A^T = [aji], obtained by interchanging rows and columns. If A is an m-by-n matrix, then A^T is an n-by-m matrix. The transpose is an involution, since (A^T)^T = A, and it interacts with multiplication via identities such as (AB)^T = B^T A^T when A and B are conformable. In linear algebra, the concept of transposition is a standard operation defined for matrices over real or complex fields; the term trasponibile may be used to emphasize that a transpose is considered or applicable in a given context.

Outside pure mathematics, trasponibile can also appear in computational or data contexts to indicate that a two-dimensional array, table, or similar structure can be rearranged by transposition. In programming and data processing, transposing data is a common operation for reorganizing rows and columns.

Etymology and related terms: the word derives from the verb transponere in Latin, and the related noun is trasposizione (the transpose). Related mathematical notions include symmetry (simmetrica) in special cases and, more generally, linear algebra concepts involving duality and index manipulation.

See also: trasposizione, matrice, trasposizione di una matrice, operatore di trasposizione.