Sentence examples for conditions for equality from inspiring English sources

As a by-product of the proof we establish precise conditions for equality.

We place emphasis on documenting necessary and sufficient conditions for equality to hold.

We give an inequality on the inertia of Hermitian matrices with some symmetry and discuss algebraic conditions for equality.

I believed that we only had to put in place the conditions for equality for the remnants of the old-fashioned sexism in our culture to wither away.

For a Steiner triple system on v points, we prove that s≤(2v+5−√24v+25)/2, and we determine necessary and sufficient conditions for equality to be attained in this bound.

Proof We first look for the conditions for equality in (16 - 17 16 - 17.

One of the advantages of these elementary proofs is that one can easily deduce the necessary and sufficient conditions for equalities.

Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.

You can check out Wikipedia for more details, but the essence is that these are classes of structures in which types (appropriately defined as Galois types) satisfy a nice locality condition for equality.

(This condition for equality is both necessary and sufficient provided that is a non-degenerate eigenvalue of U).

and a sufficient condition for equality is to have Ψ and/or MA tall and full rank.