The waring problem for matrices

DOI10.1080/03081088708817831zbMath0638.10054OpenAlexW1985450734MaRDI QIDQ3778833

David R. Richman

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1080/03081088708817831

zbMATH Keywords

Waring problem

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (8)

Matrices over non-commutative rings as sums of powers ⋮ Matrices over commutative rings as sums of higher powers ⋮ Integral matrices as diagonal quadratic forms ⋮ Matrices over noncommutative rings as sums of kth powers ⋮ Matrices over commutative rings as sums of $k$-th powers ⋮ Trace and discriminant criteria for a matrix to be a sum of sixth and eighth powers of matrices ⋮ Waring's problem for integral quaternions ⋮ Matrices over commutative rings as sums of fifth and seventh powers of matrices

Cites Work

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• Witt vectors and the algebra of necklaces
• Sums of squares in division algebras
• Sums of squares in central simple algebras
• Sums of squares of matrices
• Characterization of a class of matrices as sums of squares
• Matrices as sums of squares: a conjecture of Griffin and Krusemeyer
• Every integral matrix is the sum of three squares
• Matrices as the sum of four squares
• On the sum powers of matrices
• Matrices as sums of squares
• Solutions of x 4 + y 4 = z 4 in 2 × 2 Integral Matrices
• Solutions of A k + B k = C k in n × n Integral Matrices
• Fermat's Equation A^p+B^p=C^p for Matrices of Integers

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