Understand Hilbert Matrix for Beginners – Machine Learning Tutorial

By | August 26, 2019

Hilbert matrix is proposed by Hilbert in 1894, which is highly ill-conditioned matrix. In this tutorial, we will introduce some basic information on it.

As to each element in hilbert matrix: H(i,j)

hilbert matrix

or

hilbert matrix feature

where i≥1 and j≥1.

For example, as to 5 * 5 hilbert matrix, it is:

hilbert matrix examples

Features of hilbert matrix

  • H(i, j) = H(j, i)
  • 1 ≥ H(i, j) ≥ 0
  • It is highly ill-conditioned

 

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