$$\tilde{a} \overset{\Delta}{=} \vec{a} - \operatorname{avg}(\vec{a})\vec{1} = \mathbf{C}\vec{a}$$

Note that $$\mathbf{C}$$ is the Centering matrix.

## References#

Boyd, Stephen P., and Lieven Vandenberghe. 2018. Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares. Cambridge, UK ; New York, NY: Cambridge University Press.