In computer graphics, swizzles are a class of operations that transform vectors by rearranging components.^[1] Swizzles can also project from a vector of one dimensionality to a vector of another dimensionality, such as taking a three-dimensional vector and creating a two-dimensional or five-dimensional vector using components from the original vector.^[2] For example, if A = {1,2,3,4}, where the components are x, y, z, and w respectively, you could compute B = A.wwxy, whereupon B would equal {4,4,1,2}. Additionally, one could create a two-dimensional vector with A.wx or a five-dimensional vector with A.xyzwx. Combining vectors and swizzling can be employed in various ways. This is common in GPGPU applications^{[example needed]}.

In terms of linear algebra, this is equivalent to multiplying by a matrix whose rows are standard basis vectors. If ${\displaystyle A=(1,2,3,4)^{T}}$, then swizzling ${\displaystyle A}$ as above looks like

${\displaystyle A.wwxy={\begin{bmatrix}0&0&0&1\\0&0&0&1\\1&0&0&0\\0&1&0&0\end{bmatrix}}{\begin{bmatrix}1\\2\\3\\4\end{bmatrix}}={\begin{bmatrix}4\\4\\1\\2\end{bmatrix}}.}$

Z-order curve