Difference between revisions of "Manuals/calci/LEHMER"

Revision as of 08:39, 30 April 2015

MATRIX("LEHMER",order)

This function gives the lehmer matrix of order 3.
The the n×n Lehmer matrix, is the constant symmetric matrix defined by $a_{ij}={\frac {min{i,j}}{max{i,j}}}={\begin{cases}{\frac {i}{j}}&j\geq i\\{\frac {j}{i}}&j\gg i\end{cases}}$
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:

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-<div style="font-size:30px">'''LEHMER'''</div><br/>
+<div style="font-size:30px">'''MATRIX("LEHMER",order)'''</div><br/>
+*<math>order</math> 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 <math>a_{ij}=\frac{min{i,j}}{max{i,j}} =
+\begin{cases} \frac{i}{j} & j\ge i \\
+\frac{j}{i} & j\gg i
+ \end{cases} </math>
+*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: