# XV. On systems of linear indeterminate equations and congruences

```@article{SmithXVOS,
title={XV. On systems of linear indeterminate equations and congruences},
author={Henry John Stephen Smith},
journal={Philosophical Transactions of the Royal Society of London},
pages={293 - 326}
}```
• H. Smith
• Mathematics
• Philosophical Transactions of the Royal Society of London
The theory of the solution, in positive or negative integral numbers, of systems of linear indeterminate equations, requires the consideration of rectangular matrices, the constituents of which are integral numbers. It will therefore be convenient to explain the meaning which we shall attach to certain phrases and symbols relating to such matrices. A matrix containing p constituents in every horizontal row, and q in every vertical column, is a matrix of the type q × p. We shall employ the…
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The following essay is the third in a series devoted to the history of the theory of matrices.1 In [1975 a] I related Cauchy's important memoir on the characteristic roots of a real quadratic form to
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This book brings together all the most important known results of research into the theory of algebraic multiplicities, from well-known classics like the Jordan Theorem to recent developments such as
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• J. M. Rojas
• Mathematics, Computer Science
J. Complex.
• 2000
An algorithm for approximating the real roots of certain sparse polynomial systems with simple and efficient generalization to certain univariate exponential sums and a new and sharper upper bound on the number of connected components of a semi-algebraic set are given.