### linear transformation ⇝

## linear map

(Or "linear transformation") A function from a vector space to a vector space which respects the additive and multiplicative structures of the two: that is, for any two vectors, u, v, in the source vector space and any scalar, k, in the field over which it is a vector space, a linear map f satisfies f(u+kv) = f(u) + kf(v).

Last updated: 1996-09-30

### Nearby terms:

Linear Graph Notation ♦ linear logic ♦ **linear map** ♦ linear programming ♦ linear space

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