An Etymological Dictionary of Astronomy and Astrophysics
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In a manner characterized by first-degree algebraic terms.

Adverb of → linear.

A set of objects x₁, x₂, ..., x_n (→ vectors, → matrices, → polynomials, etc.) on a given set if there is a linear combination of them: a₁x₁ + a₂x₂ + ... + a_nx_n, which is zero, but at least one of the coefficients is non-zero. For example the binomials (2x + y) and (6x + 3y) are linearly dependent, since 3(2x + y) - (6x + 3y) = 0.

→ linearly; → dependent.

1) A set of objects x₁, x₂, ..., x_n (→ vectors, → matrices, → polynomials, etc.) if it si not → linearly dependent.
2) Of two particular solutions (y₁, y₂) of a → homogeneous linear differential equation of the second order (y^'' + a₁ y^' + a₂y = 0) on an interval [a, b], if their ratio in this interval is not a constant: y₁/y₂≠ constant.

→ linearly; → independent.

Light exhibiting → linear polarization.

→ linearly; → polarized; → light.