#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## relate

[*see also*: concern, connect, link, tie, associate, pertain, relevant

We describe how the notion of positivity relates to the other properties.

Conditions relating to bounds on the eigenvalues appear to be rare
in the literature.

Theorem 1 relates the quantity a(n) to the quantity b(n).
[*Not*: “with the quantity b(n)'']

There are numerous results in the literature relating spectral conditions
to invertibility of f.

The following proposition relates the two definitions.

There is a related result concerning primitivity.

We first replace a(n) by the related and simpler function b(n),
where......

Our results are closely related to those of Strang [5].

The above-mentioned measure is of course intimately related to the geometry of the real line.

How are these two optimality notions related? In general, they are not.

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