# 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} }

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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