Concept

Lehmer matrix

Summary
In mathematics, particularly matrix theory, the n×n Lehmer matrix (named after Derrick Henry Lehmer) is the constant symmetric matrix defined by :A_{ij} = \begin{cases} i/j, & j\ge i \ j/i, & jn. The values of elements diminish toward zero away from the diagonal, where all elements have value 1. The inverse of a Lehmer matrix is a tridiagonal matrix, where the superdiagonal and subdiagonal have strictly negative entries. Consider again the n×n A and m×m B Lehmer matrices, where m>n. A rather peculiar property of their inverses is that A−1 is nearly a submatrix of B−1, except for the A−1n,n element, which is not equal to B−1n,n. A Lehmer matrix of order n has trace n. Examples The 2×2,
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