Articulos FC INSMAT

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Combined matrices and conditioning
(2021-08-12) Máximo Santana
In this work, we study a lower bound of the condition number of a matrix by its combined matrix. In particular, we construct a special combined matrix in such a way that the sums of its columns are lower bounds of the condition number of the matrix. Cases for special matrices as unitary matrices are considered.
Combined matrix of diagonally equipotent matrices
(2023-09-12) Máximo Santana
Let (𝐴)=𝐴∘𝐴−𝑇 be the combined matrix of an invertible matrix 𝐴, where ∘ means the Hadamard product of matrices. In this work, we study the combined matrix of a nonsingular matrix, which is an 𝐻 -matrix whose comparison matrix is singular. In particular, we focus on (𝐴) when 𝐴 is diagonally equipotent, and we study whether(𝐴) is an 𝐻 -matrix and to which class it belongs. Moreover, we give some properties on the diagonal dominance of these matrices and on their comparison matrices.