On the sum powers of matrices

DOI10.1080/03081088708817800zbMath0637.10041OpenAlexW2080823918MaRDI QIDQ3778080

L.N.Vaserstein and E.R.Wheland

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1080/03081088708817800

zbMATH Keywords

sums of squaresmatrix rings

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 (10)

Matrices over non-commutative rings as sums of powers ⋮ Word equations in simple groups and polynomial equations in simple algebras. ⋮ The waring problem for matrices ⋮ 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

• Every integral matrix is the sum of three squares
• The Pythagoras number of some affine algebras and local algebras.
• Matrices as sums of squares

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