This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the. Linear Algebra and Geometry. Front Cover. Alekseĭ Ivanovich Kostrikin. Gordon and Breach Science Publishers, – Algebras, Linear – pages. I’m not sure that what I’m going to say is exactly what the author meant. However, I’ll try to explain a little of what I understand about this. First.
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Remarks regarding diagrams and graphic representations. Many general concepts and theorems of linear algebra are conveniently illustrated by diagrams and pictures. We want to warn the reader immediately about the dangers 1 of such illustrations. We live in a three-dimensional space and our diagrams usually portray two- or three-dimensional images.
In linear algebra we work with space of any finite number of dimensions and in functional analysis we work with infinite-dimensional spaces. Our “low-dimensional” intuition can be greatly developed, but it must be developed systematically 2. Here is a simple example how are we to imagine the general arrangement of two planes in four-dimensional space? What does it mean to develop such intuition systematically and how?
If someone could try to explain so that I can have a mental “picture” in my head what is actually intended by the author. Diagrams and pictures accompanying an explanation would also be greatly appreciated though one is not obligated to provide one.
I guess part of the reason why I don’t fully capture what the author is trying to ad across is because I can’t quite get my head around the example about the two planes in four dimensional space.
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I’m not sure that what I’m going to say is exactly kostgikin the author meant. However, I’ll try to explain a little of what I understand about this. First, the dangers is that sometimes when you try to take your three-dimensional intuition to higher dimensions it can break down.
You’ll tell me that they will. If you tell me that they’ll intersect you’re going to make a great mistake. There’s a kosstrikin analogy: In this case there won’t be intersection.
Home Questions Tags Users Unanswered. Linear Algebra and Geometry by Kostrikin and Manin: Remark regarding diagrams and graphic representations.
Linear Algebra and Geometry – P. K. Suetin, Alexandra I. Kostrikin, Yu I Manin – Google Books
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Linear Algebra and Geometry