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Linear Transformation

 
Sci-Tech Dictionary: linear transformation
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(′lin·ē·ər ′tranz·fər′mā·shən)

(mathematics) A function T defined in a vector space E and having its values in another vector space over the same field, such that if ƒ and g are vectors in E, and c is a scalar, then T(ƒ + g) = Tƒ + Tg and T(cƒ) = c(Tƒ). Also known as homogeneous transformation; linear function; linear operator.

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Britannica Concise Encyclopedia: linear transformation
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Home > Library > Miscellaneous > Britannica Concise Encyclopedia

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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Sci-Tech Dictionary. McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved.  Read more
Britannica Concise Encyclopedia. Britannica Concise Encyclopedia. © 2006 Encyclopædia Britannica, Inc. All rights reserved.  Read more