COMP 4107 Lecture Notes - Lecture 2: Row And Column Vectors, Linear Algebra, Mexican Peso
26 Oct 2018
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Linear algebra: motivation, need concise description of multidimensional objects, need something to describe a space, need something more than a simple real number, answer, vectors, matrices, tensors, etc. described using linear algebra, scalar. Just a number: usually give scalars lowercase variable names, examples, basic concepts the slope of a line speed of a car, vector in rn is an ordered set of n real numbers (an n dimensional number) Length of that vector in n dimensions: common norms: L1, l2 (euclidean distance in a plane: l1 norm commonly used to find difference between zero and non-zero elements. Every time an element of x moves away from 0 by , the l1 norm increases by identified by x: l2 norm finds euclidean distance from the origin to the point. The elements are referred to by xi: vector dot (inner) product, the dot product of two vectors can be rewritten in terms of norms (cid:449)he(cid:396)e is the angle between x and y.
