# 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 *a**x* + *b**y* 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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