This text aims in its early chapters to bring together all classical and recently discovered analytic relations in determinant theory. These range from the Jacobi identity, Pfaffians and Wronskians to the Cusick and Matsuno identities, the Hirota differential operator and families of distinct matrices with non-distinct determinants. Many of these relations are applied in the last chapter to give elegant proofs of the determinantal solutions of a number of nonlinear equations, of which the Kortweg-de Vries equation of wave ...
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This text aims in its early chapters to bring together all classical and recently discovered analytic relations in determinant theory. These range from the Jacobi identity, Pfaffians and Wronskians to the Cusick and Matsuno identities, the Hirota differential operator and families of distinct matrices with non-distinct determinants. Many of these relations are applied in the last chapter to give elegant proofs of the determinantal solutions of a number of nonlinear equations, of which the Kortweg-de Vries equation of wave theory is one of the simplest. Other equations include the Toda differential-difference question of lattice theory and the complex Ernst equation of general relativity.
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