Conclusion On The Abstract Approach
In principle the abstract approach can recover everything done via the traditional approach. In practice this may not seem so simple. On the other hand the notion of natural is consistent with the general covariance principle of general relativity. The latter deals with tensor fields (tensors varying from point to point on a manifold), but covariance asserts that the language of tensors is essential to the proper formulation of general relativity.
Some decades later the rather abstract view coming from category theory was tied up with the approach that had been developed in the 1930s by Hermann Weyl (in his book The Classical Groups). In a way this took the theory full circle, connecting once more the content of old and new viewpoints.
Read more about this topic: Multilinear Algebra
Famous quotes containing the words conclusion, abstract and/or approach:
“Girls who put out are tramps. Girls who don’t are ladies. This is, however, a rather archaic usage of the word. Should one of you boys happen upon a girl who doesn’t put out, do not jump to the conclusion that you have found a lady. What you have probably found is a lesbian.”
—Fran Lebowitz (b. 1951)
“When needs and means become abstract in quality, abstraction is also a character of the reciprocal relation of individuals to one another. This abstract character, universality, is the character of being recognized and is the moment which makes concrete, i.e. social, the isolated and abstract needs and their ways and means of satisfaction.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“I am always glad to think that my education was, for the most part, informal, and had not the slightest reference to a future business career. It left me free and untrammeled to approach my business problems without the limiting influence of specific training.”
—Alice Foote MacDougall (1867–1945)