SUFFICIENT DIMENSION REDUCTION BASED ON NORMAL AND WISHART INVERSE MODELS A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY LILIANA FORZANI IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY R. DENNIS COOK‚ Advisor December‚ 2007 c Liliana Forzani 2007 UNIVERSITY OF MINNESOTA This is to certify that I have examined this copy of a doctoral thesis by Liliana Forzani and have found that it is complete
Premium Variance Singular value decomposition Linear algebra
Throughout in this text V will be a vector space of finite dimension n over a field K and T : V → V will be a linear transformation. 1 Eigenvalues and Eigenvectors A scalar λ ∈ K is an eigenvalue of T if there is a nonzero v ∈ V such that T v = λv. In this case v is called an eigenvector of T corresponding to λ. Thus λ ∈ K is an eigenvalue of T if and only if ker(T − λI) = {0}‚ and any nonzero element of this subspace is an eigenvector of T corresponding to λ. Here I denotes the identity mapping
Premium Linear algebra Matrices
Initialise Clear the workspace and load Linear Algebra package > restart; > with(LinearAlgebra): If you want practice at hand calculation you should use the worksheet "Interactive Gaussian Elimination" (see Menu) Enter the matrix of coefficients and right-hand side vector You may edit the following statements or use the matrix and vector pallettes to enter new data ( see View‚ Palettes) > A:=<<4 | 2 | 3 | 2> ‚ <8 | 3 | -4 | 7> ‚ <4 | -6 | 2 | -5>>; > b:=<<15‚ 7‚ 6>>;
Premium Linear algebra
Math Summative: Fishing Rods Fishing Rods A fishing rod requires guides for the line so that it does not tangle and so that the line casts easily and efficiently. In this task‚ you will develop a mathematical model for the placement of line guides on a fishing rod. The Diagram shows a fishing rod with eight guides‚ plus a guide at the tip of the rod. Leo has a fishing rod with overall length 230 cm. The table shown below gives the distances for each of the line guides from the tip of
Premium Quadratic equation Elementary algebra Polynomial
Question 1) Evaluate without using trigonometric table: cos 75o/sin 15o + sin 12o/cos 78o – cos 18o/sin 72o (Marks 2)Question 2) Evaluate (sec2A – 1)(1 – cosec2A ) (Marks 2)Question 3) If tan A = b/a where a and b are real numbers‚ find the value of sin2 A (Marks 2)Question 4) A cricketer has mean score of 58 runs in nine innings. Find out how many runs are to be scored in the tenth innings to raise the mean score to 61. (Marks 2)Question 5) Find the mean of the following data: 46‚ 64‚ 87‚ 41‚ 58
Premium Quadratic equation Arithmetic mean Real number
“A database is a tool for collecting and organizing information ("Database Basics"‚ 2012).” This is the simplest definition of a database. A database can take many different forms‚ it can be an address book‚ a box of recipes‚ even a collection of business cards. For the purposes of this paper I will be referring to a database as the electronic version found on a computer‚ such as Microsoft Access. A database is made up of a collection of tables. These tables can be linked together to allow a user
Premium Relational model Relational database Database
Logan’s Logo So Logan has devised a logo for her company which is a square divided into 3 sections with 2 functions. Our objective is to find what functions fit the two curves on her logo and also make it fit on two other sizes of her logo. Just looking at the shape of the lines 2 types of functions immediately jump into my head‚ sinusoidal and cubic. I first traced a grid onto the original copy of the logo I was given in order to get points to start trying to form a function to match the design
Free Phase Wave Elementary algebra
2.2 Solving Quadratic Equation A quadratic equation can be solved by using: 1. Factorization i) Arrange the unknowns in general form (ax2+bx+c=0) and factorize it 2. Completing the square i) x2-6x+4=0 ii) x2-6x=-4 iii) x2-6x+-622=-4+-622 iv) x2-6x+-32=-4+-32 v) x-32=5 vi) x-3=±5 vii) x=3±5 viii) x=3+5 OR 3-5 ix) x=5.236/0.7369 3. Quadratic formula x=-b±b2-4ac2a * Forming quadratic
Premium Quadratic equation Elementary algebra Linear equation
A solid metal is dropped from the height of 64 feet. How long will it take for the solid metal to hit the ground? Ignore the air resistance. | Correct Answer: The solid metal will hit the ground in about 2 seconds. | Which of the following functions shows the graph below? | f(x) = x2 + 2x | Find the quadratic equation whose roots are 1/2 and 6. | 2x2 - 13x + 6 = 0 | The curve y = -2x2 is shifted so that its axis of symmetry is the line x = -2 and its orthogonal axis is y =
Premium Quadratic equation Real number Polynomial
QUADRATIC EQUATIONS Quadratic equations Any equation of the form ax2 + bx + c=0‚ where a‚b‚c are real numbers‚ a 0 is a quadratic equation. For example‚ 2x2 -3x+1=0 is quadratic equation in variable x. SOLVING A QUADRATIC EQUATION 1.Factorisation A real number a is said to be a root of the quadratic equation ax2 + bx + c=0‚ if aa2+ba+c=0. If we can factorise ax2 + bx + c=0‚ a 0‚ into a product of linear factors‚ then the roots of the quadratic equation ax2 + bx + c=0 can be found
Premium Quadratic equation Real number Polynomial