linear transformation

noun

Mathematics.

1. 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.

Word History and Origins

Origin of linear transformation¹

First recorded in 1885–90

Example Sentences

“What we’re seeing here is that our evolution was not entirely characterized by a linear transformation by one species to another,” Haile-Selassie added.

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A linear transformation must preserve addition and scalar multiplication: if you add something to the input, the output should change proportionally, and if you multiply the input by some particular quantity, the output should be multiplied by that quantity.

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The equation y=4x is one example of a linear transformation.

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Arnold’s cat map is a linear transformation applied over and over to a picture of a cat.

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Thus in elementary arithmetic there are the fundamental operations of the addition and the multiplication of integers; in algebra a linear transformation is an operation which may be carried out on any set of variables; while in geometry a translation, a rotation, or a projective transformation are operations which may be carried out on any figure.

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