On an extension of Fekete’s lemma

Inheung Chon

Displaying similar documents to “On an extension of Fekete’s lemma”

Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding

Jiří Rohn (2007)

Applications of Mathematics

Similarity:

For a real square matrix $A$ and an integer $d \geq 0$ , let $A_{(d)}$ denote the matrix formed from $A$ by rounding off all its coefficients to $d$ decimal places. The main problem handled in this paper is the following: assuming that $A_{(d)}$ has some property, under what additional condition(s) can we be sure that the original matrix $A$ possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists...

On the matrix negative Pell equation

Aleksander Grytczuk, Izabela Kurzydło (2009)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) $\sum_{i = 1}^{n} X ₂_{i} - d \sum_{i = 1}^{n} Y ²_{i} = - I$ with d ∈ N for nonsingular $X_{i}, Y_{i} \in M ₂ (Z)$ , i=1,...,n.

Nested matrices and inverse $M$ -matrices

Jeffrey L. Stuart (2015)

Czechoslovak Mathematical Journal

Similarity:

Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the $L U$ - and $Q R$ -factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse $M$ -matrices with symmetric, irreducible, tridiagonal inverses.

Displaying similar documents to “On an extension of Fekete’s lemma”

Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding

On the matrix negative Pell equation

Nested matrices and inverse M -matrices

Nested matrices and inverse $M$ -matrices