(M², g²ab), respectively, and if there exists an isometry.    From Wordnik.com.  [Time Machines] Reference

Further momentum is an isometry of this spacetime, so momentum is conserved.    From Wordnik.com.  [Does Space Expand?] Reference

Temperature-mediated transitions between isometry and allometry in a colonial, modular invertebarte.    From Wordnik.com.  [Biology of early life stage of tropical reef corals] Reference

Does it follow, as we would want determinism to guarantee, that Ψ is extendible to an isometry from.    From Wordnik.com.  [Time Machines] Reference

By definition a unitary operator is a bijective isometry.    From Wordnik.com.  [Discover Blogs] Reference

The shift operator on functions with a lower bounded domain is a perfect example of an isometry that is not unitary.    From Wordnik.com.  [Discover Blogs] Reference

A transformation which preserves the geometrical properties of the Euclidean spacea distance-preserving mapping or isometry.    From Wordnik.com.  [Citizendium, the Citizens' Compendium - Recent changes [en]] Reference

It is irk-some how physicists incorrectly use isometry and unitarity interchangeably when working with infinite dimensional spaces.    From Wordnik.com.  [Discover Blogs] Reference

The image of this isometry is the smallest closed subspace of H that contains the orthonormal system, which we call the (Hilbert space) span of that system.    From Wordnik.com.  [What's new] Reference

So if you assume a lower bound for time, then by definition, forward translation through time is not unitary, but it is an isometry; and reverse translation is neither since it has a non-trivial kernal.    From Wordnik.com.  [Discover Blogs] Reference

Inspired by the above exercise, we say that two inner product spaces are isomorphic if there exists an invertible isometry from one space to the other; such invertible isometries are known as isomorphisms.    From Wordnik.com.  [What's new] Reference

The image V of this isometry is the smallest closed subspace of H that contains Note the contrast here between conditional and unconditional summability (which needs only square-summability of the coefficients are absolutely summable).    From Wordnik.com.  [What's new] Reference

Now if your rocket has a spent bottom stage you can jettison that to the black hole and this isometry preserves momentum (similar to Newton’s third law) and your top stage portion will be given a huge momentum boost out of the black hole ergosphere.    From Wordnik.com.  [Be vewwwwy vewwwwy quiet….] Reference

When I try to trace her exact procedure, I get confused—even bearing in mind that some of the letters from the dedication to Pound get carried over into the section title, I can’t quite make it all match up—but I’m pretty sure there is some kind of consistent isometry between Eliot’s individual lines and hers.    From Wordnik.com.  [K. Silem Mohammad Reads Elizabeth Bachinsky] Reference

Isn’t that an isometry?.    From Wordnik.com.  [The Black Hole War] Reference