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  1. econ.upf.edu › ~michael › stanfordChapter 6 Measures of distance and correlation between variables...

    Measures of distance and correlation between variables. In Chapters 4 and 5 we concentrated on distances between samples of a data matrix, which are usually the rows. We now turn our attention to the variables, usually the columns. Two variables have a pair of values for each sample, and we can consider measures of distance and dissimilarity ...

  2. people.math.harvard.edu › ~knill › teachingUnit 1: Geometry and Distance

    Unit 1: Geometry and Distance. Lecture. 1.1. A point on the real line R is determined by a single real coordinate x. Zero 0 divides the positive axis from the negative axis. A point P = (x, y) in the plane R2 is given by two coordinates x and y. In space R3, locating a point P requires three coordinates P = (x, y, z).

  3. people.math.harvard.edu › ~knill › teachingUnit 10: Coordinates - Harvard University

    LINEAR ALGEBRA AND VECTOR ANALYSIS. MATH 22B. Unit 10: Coordinates. Introduction. 10.1. Algebra is a powerful tool in geometry. In this lecture we circle back to the concept of coordinates and look also at other coordinate systems. We have introduced space as column vectors like [1; 2; 3]T .

  4. link.springer.com › content › pdfChapter 5 Coordinate Systems - Springer

    5.1 Introduction. In this chapter we revise Cartesian coordinates, axial systems, the distance between two points in space, and the area of simple 2D shapes. It also covers polar, spherical polar and cylindrical coordinate systems.

  5. mathstats.uncg.edu › yasaki › teachingMini-Lecture 1.1 The Distance and Midpoint Formulas

    Use the Distance Formula 2. Use the Midpoint Formula. Examples: 1. Find the distance between the points (-3,7) and (4,10). 2. Determine whether the triangle formed by points A=(-2,2), B=(2,-1), and C=(5,4) is a right triangle. 3. Find the midpoint of the line segment joining the points P1=(6,-3) and P2=(4,2).

  6. www.adelaide.edu.au › mathslearning › uaTopic 2 Linear Functions - The University of Adelaide

    The equation of a line is a formula showing the relationship between the x- and y-coordinates of any point P on the line. Suppose a line has gradient m and y -intercept (0, c ), and suppose that the point P is a general point

  7. people.math.harvard.edu › ~knill › teachingUnit 4: Lines and Planes - Harvard University

    is the distance between the two lines L and M. Proof: the distance is the length of the vector projection of PQ~ onto ~u ~v which is normal to both lines. For example, to compute the distance between ~r(t) = (2;1;4) + t( 1;1;0) and M is the line ~s(t) = ( 1;0;2) + t(5;1;2) form the cross product of [ 1;1;0] and [5;1;2] is [2;2; 6]. The