How can I store rotating index in a square matrix?

For example, if I have index [1,2,3,4] how can I store it in a matrix such that each column represent these indices in rotation:

A = [1 2 3 4;

        2 3 4 1;

        3 4 1 2;

        4 1 2 3];

Furthermore, the index I have is quite huge, which means A will can be a 1024 x 1024 in dimension.

Answer 1

[MathWorks Support Team]

You can use the "hankel" function to create such matrix in MATLAB:

>> v = 1:4;
>> A = hankel(v, circshift(v,1))

Furthermore, the matrix A above is actually a skew-circulant matrix, which is a special type of Hankel matrix. In real-life application, these matrices rarely need to be explicitly computed, as they can be applied via cross-correlations (and especially in the case of a skew-circulant matrix, this can be done quite efficiently with the FFT).