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A linear equation is an equation in the form:
- $b = a_1 x_1 + a_2 x_2 + \cdots + a_n x_n$
where all of $a_1, \ldots, a_n, x_1, \ldots x_n, b$ are elements of a given field.
The point is that all the indices of the $x$ and $y$ terms in such an equation are $1$.
- 1954: A.C. Aitken: Determinants and Matrices (8th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions and Fundamental Operations of Matrices: $2$. Linear Equations and Transformations
- 1987: A.G. Hamilton: A First Course in Linear Algebra ... (next): $1$: Gaussian Elimination
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $4$: Lure of the Unknown: Equations
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: linear equation