Editing Hankel matrix (section)

==Hankel matrix transform==
{{Distinguish|Hankel transform}}

The '''Hankel matrix transform''', or simply '''Hankel transform''', of a [[sequence]] <math>b_k</math> is the sequence of the determinants of the Hankel matrices formed from <math>b_k</math>. Given an integer <math>n > 0</math>, define the corresponding <math>(n \times n)</math>-dimensional Hankel matrix <math>B_n</math> as having the matrix elements <math>[B_n]_{i,j} = b_{i+j}.</math> Then the sequence <math>h_n</math> given by 
<math display="block">
 h_n = \det B_n
</math>
is the Hankel transform of the sequence <math>b_k.</math> The Hankel transform is invariant under the [[binomial transform]] of a sequence. That is, if one writes
<math display="block">
 c_n = \sum_{k=0}^n {n \choose k} b_k
</math>
as the binomial transform of the sequence <math>b_n</math>, then one has <math>\det B_n = \det C_n.</math>