Algosim documentation: antidiagonal

antidiagonal

Represents the antidiagonal in a matrix.

Syntax

The returned value is an lvalue.

Description

If A is a square matrix then antidiagonal(A) represents the antidiagonal in A, that is, the entries A[i, j] where i = n − j + 1 where n is the size of A, from the top-right to the bottom-left corner.

Typewise, antidiagonal(A) is a vector.

antidiagonal(A) is an lvalue, so it may be assigned to. If A is a real matrix, then only a real vector can be assigned to it.

Examples

A ≔ ❨❨5, 2, 1❩, ❨3, 6, 9❩, ❨0, 2, 1❩❩
⎛5  2  1⎞
⎜3  6  9⎟
⎝0  2  1⎠

antidiagonal(A)
 ⎛1⎞
e⎜6⎟
 ⎝0⎠

antidiagonal(A) ≔ ❨3, 9, 4❩
 ⎛3⎞
e⎜9⎟
 ⎝4⎠

A
⎛5  2  3⎞
⎜3  9  9⎟
⎝4  2  1⎠

See also