Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems.
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Add to Cart Add to Cart. Add to Wishlist Add to Wishlist. The basic structure playing the key role in this book is a real inner product space X,? R,a so-called inner product, satisfying rules i , ii , iii , iv of section 1 of chapter 1.
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In order to avoid uninteresting cases from the point of view of geometry, we will assume throughout the whole book that there exist elements a,b in X which are linearly independent. But, on the other hand, we do not ask for the ex- tence of a positive integer n such that every subset S of X containing exactly n elementsislinearlydependent.
Inotherwords,wedonotassumethatX isa? So, when dealing in this book with di?
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In fact, it plays no role, whatsoever, in our considerations whether the dimension ofX is? In this sense we maysaythat our presentationin question isdimension-free. The prerequisites for a fruitful reading of this book are essentially based on the sophomore level, especially after mastering basic linear algebra and basic 2 3 geometry ofR andR.
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