What is the name (for example, Vandermonde determinant) of the matrix or determinant showed by the following picture? I believe that it should have a name, but I am not sure.
Dear Feng Qi,
I never heard that this kind of determinants has a special name, but if you subtract n-th row from (n+1)-th row, then (n-1)-th row from n-th row, ... , 1-st row from 2-nd row, you'll get a tridiagonal determinant. Best regards, Yuri
The matrix is a lower Hessenberg matrix, since all the entries above the superdiagonal are zero.
Definition. A matrix H = (hij)nxn is called a lower (upper) Hessenberg matrix if hij = 0 for all pairs (i, j) such that i + 1 < j (j + 1 < i).
The matrix (determiant) is a special form of lower Hessenberg matrix (determinant), as Sophie above commented.
The above matrix is a "bi-diagonal companion matrix," say.
We have a new information:
S.J. Kirkland and M. Neumann, Group Inverses of M-matrices and their Applications, CRC Press Taylor & Francis Group, Boca Raton, 2013.
p.48. Equation (4.1). The matrix is known as the "population projection matrix".
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