However, in projective geometry every conic section is equivalent to an ellipse.

However, as René Descartes noticed, perceptual space has a projective geometry, things within it appear as if they are viewed from a point.

However, as noted above, finitely generated nonzero modules have maximal submodules, and also projective modules have maximal submodules.

However, using projective geometry, so that R < sup > 2 </ sup > is considered to be a subset of R < sup > 3 </ sup >, translations become affine linear transformations.

However, many practitioners continue to rely on projective testing, and some testing experts ( e. g., Cohen, Anastasi ) suggest that these measures can be useful in developing therapeutic rapport.

However, it is an elementary result, which can be seen concretely as follows: the set of normal subgroups of a given index p form a projective space, namely the projective space

However, infinity is a metric concept, so a purely projective geometry does not single out any points, lines or plane in this regard — those at infinity are treated just like any others.

However, in dimension two there are affine and projective planes which are not isomorphic to Galois geometries, namely the non-Desarguesian planes.

However, one cannot take the projectivization of an affine space, so projective spaces are not naturally quotients of affine spaces: one can only take the projectivization of a vector space, since the projective space is lines through a given point, and there is no distinguished point in an affine space.

However, one can lift a projective representation of G to a linear representation of a different group C, which will be a central extension of G. To understand this, note that GL ( V ) → PGL ( V ) is a central extension of PGL, meaning that the kernel is central ( in fact, is exactly the center of GL ).

However, there are examples of finitely generated modules over a non-Noetherian ring which are locally free and not projective.

However, with the exception of the non-Desarguesian planes, all projective spaces are the projectivization of a linear space over a division ring though, as noted above, there are multiple choices of linear structure, namely a torsor over ( for ).

However, under the assumption of projective determinacy, all projective sets have both the perfect set property and the property of Baire.

However, IFSs may also be built from non-linear functions, including projective transformations and Möbius transformations.

However, one can take a projective limit of finite constant group schemes to get profinite group schemes, which appear in the study of fundamental groups and Galois representations or in the theory of the fundamental group scheme, and these are affine of infinite type.

If f is quasi-compact and L is an invertible sheaf on X, then L is f-ample or f-very ample if and only if its pullback L ′ is f ′- ample or f ′- very ample, respectively .< ref > EGA IV < sub > 2 </ sub >, Corollaire 2. 7. 2 .</ ref > However, it is not true that f is projective if and only if f ′ is projective.

However, the spin factors play a role in special relativity, and all the formally real Jordan algebras are related to projective geometry.

However, proved a complex-number analogue of the Sylvester – Gallai theorem: whenever the points of a Sylvester – Gallai configuration are embedded into a complex projective space, the points must all lie in a two-dimensional subspace.

However, the simple modules with characteristic dividing the group order are rarely projective.

However they do teach a subject called " Modern Studies " which covers the social, political and economic study of local, national and international issues.

However, in contrast to the countries in the Anglo-Saxon system category, this is a much more widespread network of collective agreements, which covers most industries and most firms.

However, they exclude Chronicles, which covers the same period, as well as Ruth.

However, local Indians had evidently looted the hiding place, and White found " about the place many of my things spoyled and broken, and my books torne from the covers, the frames of some of my pictures and mappes rotten and spoyled with rayne, and my armour almost eaten through with rust "

However, in contrast to this Ian MacDonald, in his book Revolution in the Head: The Beatles ' Records and the Sixties, calls it " One of The Beatles best covers ".

However, the " Bryn Mawr " zip code ( 19010 ) covers a larger area, and as a result, the geographic term " Bryn Mawr " is often used in a sense that includes not only the CDP, but also other areas that share the zip code.

However it is more common in aftermarket that visual aesthetics take on a more significant role in design than other types of sub drivers, including high contrast paint schemes, grill covers, translucent or refractive materials.

However, Snaresbrook Ward in the London Borough of Redbridge covers most of Wanstead High Street.

However, the actual community that is considered to be Golden Valley covers a larger area than the CDP defined by the Census Bureau.

However, photonics covers a huge range of science and technology applications, including: laser manufacturing, biological and chemical sensing, medical diagnostics and therapy, display technology, and optical computing.

However, in that same year the collection Heavy Hitters, a set of covers featuring Schenker and a revolving group of heavy metal all-stars, was marketed as a Michael Schenker Group album, with the result that Schenker only received a flat fee.

However, it has two graph-theoretic interpretations: as the sum of weights of cycle covers of a directed graph, and as the sum of weights of perfect matchings in a bipartite graph.

However, covers of famous old songs sounds chaotically effective ( especially " Manic Monday ").

However, the " magic notes " logo is occasionally used, usually to give a ' retro ' feel ( such as the 2008 MGMT singles that use the " magic notes " on the vinyl labels but the " walking eye " on the covers ).

However, lingerie, non-offensive covers of adult material, etc.

However, it only covers news of the day but not past issues.

However, the programme also covers more ' difficult ' or less-widely known composers, with weeks devoted to Rubbra, Medtner, Havergal Brian and the Minimalists among others.

However, after several rehearsals King believed " things didn't pan out " with heavy metal covers, so the band decided to cover punk songs.

However, the English word covers two concepts which can be quite distinct: religious and spiritual enlightenment () and secular or intellectual enlightenment ( German: Aufklärung ).

However, most of the regular bands played one or two covers during their sets.

However, additional asphalt covers are used on most 400-series highways because the asphalt is more resistant to erosion from de-icing salt than concrete.

However slips in the complicated process of production, some detailed below, mean that the finished covers do not quite exhibit the intended proportions, and are both slightly out of true in some respects.

However, this section covers the status of Rose Bowl agreements from the collapse of the PCC until the BCS era and the AAWU was not known by its current name during this period.

However, the LC update saw the SL / E specification downgraded from alloy wheels to steel wheels with plastic wheel covers.

However, it covers much of the valley floor around and beneath Cropston Reservoir, – demonstrating that the present Lin valley was also there 220 million years ago.