On the matrix equation \(f(x)=A\)

DOI10.1016/0024-3795(92)90390-VzbMath0753.15009MaRDI QIDQ1183203

Frank Uhlig, Jean-Claude Evard

Publication date: 28 June 1992

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

solutionsminimal polynomialmatrix equationholomorphic matrix equation

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

Related Items

Comparison of the sets of polynomials \(p\) and \(q\) such that \(X=p(A)\) and \(Y=q(B)\) are solutions of the matrix equations \(f(X)=A\) and \(f(Y)=B\) ⋮ Computing primary solutions of equations involving primary matrix functions ⋮ Uniqueness of matrix \(m\)th root ⋮ A Galois approach to \(m\)th roots of matrices with rational entries ⋮ Two results about the matrix exponential ⋮ The image of polynomials in one variable on the algebra of \(3 \times 3\) upper triangular matrices ⋮ Solutions of the matrix equation \(p(X)=A\), with polynomial function \(p(\lambda)\) over field extensions of \(\mathbb{Q}\) ⋮ Substitution algorithms for rational matrix equations ⋮ Unnamed Item ⋮ Extraction of \(n\)th roots of \(2 \times 2\) matrices ⋮ Commutators and powers of infinite unitriangular matrices. ⋮ Structure of the \(n\)th roots of a matrix

Cites Work

• Extraction of mth roots in matrix rings over fields
• Practical computation of matrix functions
• Inertia characteristics of self-adjoint matrix polynomials
• On the matrix roots of \(f(X)=A\)
• Semi-stability of sums of partial multiplicities under additive perturbation
• Roots of real matrices
• A faster, more stable method for comuting the pth roots of positive definite matrices
• Explicit polar decomposition and a near-characteristic polynomial: the \(2\times 2\) case
• A NOTE ON MATRIX POLYNOMIALS
• The Matrix Equation X 2 - I = 0 Over a Finite Field
• The Square Root of a 2 × 2 Matrix
• Themth Power of an$n \times n$ Matrix and the Bell Polynomials
• Which Real Matrices Have Real Logarithms?
• Square roots of complex matrices
• Some Theorems on Commutative Matrices
• The Equivalence of Definitions of a Matric Function
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