linear transformation


linear transformation

noun

Definition of LINEAR TRANSFORMATION

1
:  a transformation in which the new variables are linear functions of the old variables
2
:  a function that maps the vectors of one vector space onto the vectors of the same or another vector space with the same field of scalars in such a way that the image of the sum of two vectors equals the sum of their images and the image of the product of a scalar and a vector equals the product of the scalar and the image of the vector

First Known Use of LINEAR TRANSFORMATION

circa 1846

linear transformation

noun    (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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