Is every nonsingular matrix diagonally equivalent to a matrix with all distinct eigenvalues?
نویسندگان
چکیده
منابع مشابه
On the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues
Consider an n × <span style="fon...
متن کاملIs Every Matrix Similar to a Toeplitz Matrix?
We show that every n × n complex nonderogatory matrix is similar to a unique unit upper Hessenberg Toeplitz matrix. The proof is constructive, and can be adapted to nonderogatory matrices with entries in any field of characteristic zero or characteristic greater than n. We also prove that every n× n complex matrix with n ≤ 4 is similar to a Toeplitz matrix.
متن کاملon the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues
consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...
متن کاملMatrices Diagonally Similar to a Symmetric Matrix
Let IF be field, and let A and B be n X n matrices with elements in IF. Suppose that A is completely reducible and that B is symmetric. If the principal minors of A determined by the 1and 2-circuits of the graph of B and by the chordless circuits of the graph of A are equal to the corresponding principal minors of B, then A is diagonally similar to B; and conversely.
متن کاملA stable test to check if a matrix is a nonsingular M-matrix
A stable test for checking if a matrix is a nonsingular M -matrix is presented. Its computational cost is, in the worst case, O(n2) elementary operations higher than the computational cost of Gaussian elimination. The test can be applied to check if a nonnegative matrix has spectral radius less than 1.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.06.032