antidiagonals

In linear algebra, an antidiagonal is a diagonal of a square matrix where the sum of the row and column indices is constant. For an n x n matrix A, the elements A[i][j] are on an antidiagonal if i + j = k for a fixed integer k. The possible values for k range from 1 to 2n-1. The main antidiagonal, also known as the anti-diagonal or counter-diagonal, consists of elements where i + j = n + 1. For example, in a 3x3 matrix, the main antidiagonal elements are A[1][3], A[2][2], and A[3][1].

Antidiagonals are distinct from the main diagonal, where the row and column indices are equal (i = j), and other diagonals where the difference between row and column indices is constant (i - j = constant). The concept of antidiagonals is particularly relevant in certain matrix operations and theoretical contexts, though less frequently encountered than the main diagonal. Some matrix transformations or definitions might specifically refer to the elements lying on these lines. The order of elements along an antidiagonal is typically considered from top-right to bottom-left.