Alternant matrix

An alternant matrix is a special kind of square matrix where every other diagonally adjacent pair of elements (starting from the top-left corner) have the opposite sign. It's like a checkerboard, where every other tile is a different color.

For example, in a 3x3 alternant matrix, the elements would look like:

1 -2 3
2 -4 2
3 -2 1

Notice how the top-left to bottom-right diagonal has only positive elements, and the other diagonal has only negative elements. The same pattern repeats for larger alternant matrices.

Alternant matrices have some interesting mathematical properties, such as being diagonalizable (which makes them easier to work with) and having eigenvalues equal to the sum or difference of the elements on the two diagonals.

So, think of an alternant matrix as a special kind of square matrix with a checkerboard-like pattern of positive and negative elements on the diagonals.