Manuals/calci/LEHMER

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MATRIX("LEHMER",order)


  • is the order of the Lehmer matrix.

Description

  • This function gives the lehmer matrix of order 3.
  • The the n×n Lehmer matrix, is the constant symmetric matrix defined by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{ij}=\frac\left \{min {i,j}\right\}\left\{{max {i,j}\right\ } = \begin{cases} \frac{i}{j} & j\ge i \\ \frac{j}{i} & j > i \end{cases} }
  • Also the inverse of a Lehmer matrix is a tridiagonal matrix and is known to be symmetric tridiagonal.
  • And the value of this matrix have strictly negative entries (i.e., with positive eigenvalues).
  • Example of 2x2 and 3x3 lehmer matrices and its inverses are