MATH 307 Lecture Notes - Lecture 3: Institution Of Engineering And Technology, Lp Space
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A norm of a vector is a generalization of size of vectors. I length of v i z t 12 55. The lengthof vector is a norm called euclidean norm allnorms have important properties that capture the notion oflength. A norm h h on a vector is a real valued function satisfying the following conditions. 121 11 11 scaled by abs value of scalar 2. Euclidean norm or h norms on r for. 2 co not a norm l f x. Ext check this for h s 12 norms. 11 11 e hxhz e il x il vx. Defn similar to vectornorms except thevectors x y should be replaced bya b. 11allhs iet idij12 i thnow j th column eg a if. An mxn matrix a can be thought as a map rn 7 rm. Let"s assume we use the same typeof norm for. 11 allop under map a so 11allop is the maximum stretching factor of map a.
