It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.
This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.
I am opposed to textbooks... I find it hateful to give a course where I have to plough my way through chapter after chapter of a given book. The liveliness of the lecture, which is meant to give an impetus to the sudents, would suffer tremendously.
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