Magic square spectra

DOI10.1016/j.laa.2008.10.032zbMath1173.05011OpenAlexW2037787135MaRDI QIDQ1017627

Peter Loly, Walter Trump, Daniel Schindel, Ian T. Cameron

Publication date: 12 May 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.10.032

zbMATH Keywords

singularitieseigenvaluesvector spacescharacteristic equationsmagic squaresdiagonabilityFrénicle and Schroeppel complete sets

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Orthogonal arrays, Latin squares, Room squares (05B15) Eigenvalues, singular values, and eigenvectors (15A18) Matrices of integers (15B36) Vector spaces, linear dependence, rank, lineability (15A03) Recreational mathematics (00A08) Matrices, determinants in number theory (11C20)

Related Items (11)

On the algorithmic complexity of zero-sum edge-coloring ⋮ A fast algorithm for computing the number of magic series ⋮ Some results on magic squares based on generating magic vectors and R-C similar transformations ⋮ Compound Lucas magic square matrices ⋮ A GENERALIZATION OF NONSINGULAR REGULAR MAGIC SQUARES ⋮ On nonsingular regular magic squares of odd order ⋮ On properties of special magic square matrices ⋮ Vector spaces of new special magic squares: reflective magic squares, corner magic squares, and skew-regular magic squares ⋮ A construction of regular magic squares of odd order ⋮ Spectra of order-4 special magic squares ⋮ Some stochastic properties of ``semi-magic and ``magic Markov chains

Uses Software

• Matlab
• Survo

Cites Work

• Group inverses of \(M\)-matrices associated with nonnegative matrices having few eigenvalues
• Even Order Regular Magic Squares Are Singular
• Cubic polynomials, their roots and the Perron-Frobenius theorem
• 2617. Magic matrices
• Characteristic Roots of Semi-Magic Square Matrices
• Characteristic Polynomials of Magic Squares
• Enumerating the bent diagonal squares of Dr Benjamin Franklin FRS
• Matrix Analysis
• Magic squares of order four
• Old Magic Powers
• Semi-magic squares and their orthogonal complements
• The Probability that a Matrix of Integers Is Diagonalizable
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