Reversing the order of, say columns, we get a square  Toeplitz sub matrix of the form 

M_{j,l} =  b_(l-j} ,  where    b_i :=  a_{-i +k}  ;

For say m-diagonal matrices of m

 Dear prof. Joachim Domsta,

Thank you for your very nice and useful answer!

Regards,

Joseph 

My answer comes a year later, though - this is a Hankel Matrix. It is a cousin of Toeplitz matrix.

Let me comment the last interesting Viera's answer: As LadyWiki states, the matrices with elements [a_{j-k}: . . . ] are not Hankel, unless the sequence is constant. Indeed, the Hankel matrices are of the form [b_{j+k-2}:...] and they have necessarily equal elements on the parallel "antidiagonals" (i.e. if j+k = const), whereas the Toeplitz matrices are constant along the parallel "diagonals" (if j-k=const). Surely, these two types can be called cousins:)

Best regards, Joachim

LadyWiki? I never heard about it :)

Dear Joachim, I think we both agree that the matrix in question is Hankel.

x3 makes the shape slightly missleading ... but in fact, the antidiagonals are constant. This is stressed by the term shifted matrix as well.