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:
“The conclusion has never changed: the worst sort of people come here for the worst sort of reasons and put upon those of us who have conveniently forgotten where we came from and how we got here.”
—Anna Quindlen (b. 1952)
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“There is no calm philosophy of life here, such as you might put at the end of the Almanac, to hang over the farmer’s hearth,—how men shall live in these winter, in these summer days. No philosophy, properly speaking, of love, or friendship, or religion, or politics, or education, or nature, or spirit; perhaps a nearer approach to a philosophy of kingship, and of the place of the literary man, than of anything else.”
—Henry David Thoreau (1817–1862)