The Costas condition on a permutation matrix, expressed as row indices as elements of a vector c, can be expressed as A*c=b, where b is a vector of integers in which no element is zero.  A particular formulation of the matrix A allows a singular value decomposition in which the eigenvalues are squared integers and the eigenvalues may be scaled to vectors with all integer elements.  This is a database of the Costas constraint matrices A, the scaled eigenvectors, and the squared eigenvalues for orders 3 through 100.

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[1] James Beard, "Database of Singular Value Decompositions of Matrix Representations of the Costas Condition", IEEE Dataport, 2020. [Online]. Available: http://dx.doi.org/10.21227/h498-px29. Accessed: Apr. 13, 2024.
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url = {http://dx.doi.org/10.21227/h498-px29},
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title = {Database of Singular Value Decompositions of Matrix Representations of the Costas Condition},
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James Beard. (2020). Database of Singular Value Decompositions of Matrix Representations of the Costas Condition. IEEE Dataport. http://dx.doi.org/10.21227/h498-px29
James Beard, 2020. Database of Singular Value Decompositions of Matrix Representations of the Costas Condition. Available at: http://dx.doi.org/10.21227/h498-px29.
James Beard. (2020). "Database of Singular Value Decompositions of Matrix Representations of the Costas Condition." Web.
1. James Beard. Database of Singular Value Decompositions of Matrix Representations of the Costas Condition [Internet]. IEEE Dataport; 2020. Available from : http://dx.doi.org/10.21227/h498-px29
James Beard. "Database of Singular Value Decompositions of Matrix Representations of the Costas Condition." doi: 10.21227/h498-px29