Sentence examples for condition for equality from inspiring English sources

(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.

Applying Lemma 1 to analyze the condition for equality of the first inequality in Equation 10, we get the necessary and sufficient conditions for equality as stated in this theorem for the case of.

end{aligned} (2.8 By the condition for equality in (2.7), there is equality in (2.8) if and only if ((Y^{p/2}Z^{Y^{p/2})^{1/p}) and Y commute, and evidently this is the case if and only if Z and Y commute.

The idea that standardized testing is a necessary condition for equality in the classroom, that "kids who aren't tested are kids who don't count," can only live if testing lives.

Part 2: Equality is attained by parabolas and the condition for equality in Eq. (38) is where the ability to measure the ratio of parallel lines in the affine plane is used.

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.

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.

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

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