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6 Nov 2019
In proving the Pythagorean theorem in class, we saw that |u vector + v vector |^2 = ||u vector ||^2 + 2 u vector middot v vector + ||v vector ||^2. Moreover, from the "physics'" definition of the dot-product, i.e. u vector middot v vector = ||u vector || ||v vector || cos (theta) and the fact that cos (theta) lessthanorequalto 1, it is obvious that u vector middot v vector lessthanorequalto ||u vector|| ||v vector|| (called the Schwarz inequality). Use both of the above properties of dot-products and norms to prove the triangle inequality. All stops must follow loyally from one another, and must be justified. Show transcribed image text
In proving the Pythagorean theorem in class, we saw that |u vector + v vector |^2 = ||u vector ||^2 + 2 u vector middot v vector + ||v vector ||^2. Moreover, from the "physics'" definition of the dot-product, i.e. u vector middot v vector = ||u vector || ||v vector || cos (theta) and the fact that cos (theta) lessthanorequalto 1, it is obvious that u vector middot v vector lessthanorequalto ||u vector|| ||v vector|| (called the Schwarz inequality). Use both of the above properties of dot-products and norms to prove the triangle inequality. All stops must follow loyally from one another, and must be justified.
Show transcribed image text Collen VonLv2
5 May 2019