linear transformation

linear transformation
a map from one vector space to a vector space having the same field of scalars, with the properties that the map of the sum of two vectors is the sum of the maps of the vectors and the map of a scalar times a vector equals the scalar times the map of the vector. Also called linear function.
[1885-90]

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In mathematics, a rule for changing one geometric figure (or matrix or vector) into another using a formula with a specified format.

The format must be a linear combination, in which the original components (e.g., the x and y coordinates of each point of the original figure) are changed via the formula ax + by to produce the coordinates of the transformed figure. Examples include flipping the figure over the x or y axis, stretching or compressing it, and rotating it. Every such transformation has an inverse, which undoes its effect.

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Universalium. 2010.

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