An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

1) General: Determined or conditioned by something else.
2) Math.: A variable whose value depends on the value assigned to another variable.
3) Statistics: An event which is not independent.

M.E. dependant, from M.Fr., pr.p. of dépendre, from L. dependere, from → de- + pendere "to hang, be suspended," PIE base *(s)pen(d)- "to pull, stretch."

Vâbasté, from vâ-→ de- + basté p.p. of bastan "to bind, shut," from Mid.Pers. bastan/vastan "to bind, shut," Av./O.Pers. band- "to bind, fetter," banda- "band, tie," cf. Skt. bandh- "to bind, tie, fasten," PIE *bhendh- "to bind" (Ger. binden, E. bind).

Math.: A variable whose value depends on the value assigned to another value. For example, in the equation y = 2x, the value of y depends on that of x. See also → independent variable.

→ dependent; → variable.

Not dependent.

From negation prefix → in- + → dependent.

Statistics: Two events if the occurrence of one of them gives no → information about whether or not the other event will occur; these events have no influence on each other.

→ independent; → event.

Statistics: Two random variables X and Y if and only if the value of X has no influence on the value of Y and vice versa.

→ dependent; → random; → variable.

Math.: A variable whose value determines the value of other variables. For example, x, in the expression y = f(x), is the independent variable. See also → dependent variable.

→ independent; → variable.

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.