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Written by one of America's most influential teachers, this text presents the fundamentals of higher algebra and a thorough foundation in algebraic principles. Beginning with an account of polynomials and their basic properties, it examines determinants and Laplace's development, multiplication theorem, bordered and adjoint determinants, the theory of linear dependence, linear equations, and related topics. A treatment of theorems concerning the rank of a matrix is followed by chapters on linear transformations and the combination of matrices, invariant and bilinear forms. Additional topics include quadratic forms, factors of polynomials, theorems on integral rational invariants, and elementary divisors