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:
“It is a great many years since at the outset of my career I had to think seriously what life had to offer that was worth having. I came to the conclusion that the chief good for me was freedom to learn, think, and say what I pleased, when I pleased. I have acted on that conviction... and though strongly, and perhaps wisely, warned that I should probably come to grief, I am entirely satisfied with the results of the line of action I have adopted.”
—Thomas Henry Huxley (1825–95)
“What is important, then, is not that the critic should possess a correct abstract definition of beauty for the intellect, but a certain kind of temperament, the power of being deeply moved by the presence of beautiful objects.”
—Walter Pater (1839–1894)
“The minute you try to talk business with him he takes the attitude that he is a gentleman and a scholar, and the moment you try to approach him on the level of his moral integrity he starts to talk business.”
—Raymond Chandler (1888–1959)