বুঝাও (Teach Me)

LINEAR ALGEBRA (Part-6) Norms Norms Norm is used to measure the size/length/magnitude/distance of a vector. Like for example we know the Normal distance between two points x 1 =2 and x 2 =4 is x 2 -x 1 =4-2=2 Another example is the Euclidean distance between two points x 1 =2 and x 2 =4 is √(4-2) 2 =2 In general Norm is written by L P norm = ||x|| p = (∑|x i | p ) 1/p Where p = 1 or 2 L 1 Norm The L 1 norm is calculated as the sum of the absolute vector values. Let's put 1 in the above general norm equation. Here p=1 as L 1 Norm. ||x|| p = (∑|x i | p ) 1/p ||x|| 1 = (∑|x i | 1 ) 1/1 ||x|| 1 = ∑|x i | So it is just the sum of the absolute vector values. consider vector v = [1 -2 6] ||v|| 1 = |1| + |-2| + |6| = 1+2+6 = 9 L 2 Norm It is also called Euclidean norm. The L 2 norm is calculated as root over of the sum of the squared vector values. Let's put 2 in the above general norm equation.