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:
“I have come to the conclusion that the closer people are to what may be called the front lines of government ... the easier it is to see the immediate underbrush, the individual tree trunks of the moment, and to forget the nobility the usefulness and the wide extent of the forest itself.... They forget that politics after all is only an instrument through which to achieve Government.”
—Franklin D. Roosevelt (18821945)
“We are all hungry and thirsty for concrete images. Abstract art will have been good for one thing: to restore its exact virginity to figurative art.”
—Salvador Dali (19041989)
“The nearer people approach old age the closer they return to a semblance of childhood, until the time comes for them to depart this life, again like children, neither tired of living nor aware of death.”
—Desiderius Erasmus (c. 14661536)