Difference between revisions of "Manuals/calci/LEHMER"
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*The the n×n Lehmer matrix, is the constant symmetric matrix defined by <math>a_{ij}=\frac{min{i,j}}{max{i,j}} = | *The the n×n Lehmer matrix, is the constant symmetric matrix defined by <math>a_{ij}=\frac{min{i,j}}{max{i,j}} = | ||
\begin{cases} \frac{i}{j} & j\ge i \\ | \begin{cases} \frac{i}{j} & j\ge i \\ | ||
| − | \frac{j}{i} & j\ | + | \frac{j}{i} & j\g i |
\end{cases} </math> | \end{cases} </math> | ||
*Also the inverse of a Lehmer matrix is a tridiagonal matrix and is known to be symmetric tridiagonal. | *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). | *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: | *Example of 2x2 and 3x3 lehmer matrices and its inverses are: | ||
Revision as of 08:39, 30 April 2015
MATRIX("LEHMER",order)
- is the order of the Lehmer matrix.
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 (unknown function "\g"): {\displaystyle a_{ij}=\frac{min{i,j}}{max{i,j}} = \begin{cases} \frac{i}{j} & j\ge i \\ \frac{j}{i} & j\g 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: