Consider the generic matrix $A$,
$$\pmatrix{a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{m1}&a_{m2}&\cdots&a_{mn}\\}$$
where each $a_{ij} \in \mathbb{R}$. I'll say that row $k$ "dominates" row $l$ if $\forall j\le n: a_{kj} \ge a_{lj}$ (please correct my terminology here).
I would like to generate a new matrix $B$ which is the same as $A$, except that all the dominated rows are removed. I have a large matrix ($A$) with a hundred million entries or so and would like to transform it to a smaller matrix ($B$) to save computing time on subsequent operations. I'm looking for a computationally efficient algorithm for accomplishing this.
References and terminology are appreciated.