On a bound for the Hadamard product of an M-matrix and its inverse Linear Algebra Appl., 144 (1991), pp. 171-178 View in ScopusGoogle Scholar [6] D.M. Young Iterative Solution of Large Linear Systems, Academic Press, New York (1971) Google ScholarCited...
Some new lower bounds of the minimum eigenvalue of the Hadamard product of a M-matrix and its inverse are given. These bounds have improved the results of related studies. The estimating formulas of the bounds only depend on the entries of matrices; therefore,they are easy to calculate.关键...
Invertible matrix, a square matrix such that the product of the matrix and its inverse generates the identity matrix. That is, a matrix M, a general n × n matrix, is invertible if, and only if, M ∙ M−1 = In, where M−1 is the inverse of M and In
For the Hadamard productA∘A−1of anM-matrixAand its inverseA−1, we give new lower bounds for the minimum eigenvalue ofA∘A−1. These bounds are strong enough to prove the conjecture of Fiedler and Markham [An inequality for the Hadamard product of anM-matrix and inverseM-matrix...
In this paper, combining the equivalent form of the unified coupled algebraic Riccati equation (UCARE) with the eigenvalue inequalities of a matrix's sum and product, using the properties of an M-matrix and its inverse matrix, we offer new lower and upper matrix bounds for the solution of ...
The inverse of a matrix A is A⁻¹, just as the inverse of 2 is ½. We can solve equations by multiplying through by inverses; it's similar with matrices.
Finding the Multiplicative Inverse Using Matrix MultiplicationWe can now determine whether two matrices are inverses, but how would we find the inverse of a given matrix? Since we know that the product of a matrix and its inverse is the identity matrix, we can find the inverse of a matrix ...
the inverse of a matrix
Example: For matrix , its inverse is since AA-1 = and A-1A = .Here are three ways to find the inverse of a matrix:1. Shortcut for 2x2 matrices For , the inverse can be found using this formula: Example: 2. Augmented matrix method Use Gauss-Jordan elimination to transform [ A...
Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the ...