Publications by Emmanuel Hayble-Gomes
Data 605-Homework4
Problem 1 In this problem, we’ll verify using R that SVD and Eigenvalues are related as worked out in the weekly module. Given a 3 x 2 matrix A write code in R to compute \(X = AA^T\) and \(Y = A^TA\). Then, compute the eigenvalues and eigenvectors of X and Y using the built-in commands in R. \[A=\begin{bmatrix}1&2&3\\-1&0&4\end{bmatrix}\] Then...
2129 sym R (1410 sym/10 pcs) 2 tbl
Data 605-Discussion4
Problem C43 Define the following: \[ T:p_3 \rightarrow p_2\\by\\T(a+bx+cx^{2}+dx^{3})=b+2cx+3dx^{2} \] Find the pre-image of 0. Does this linear transformation seem familiar? Let the following be the preimage of T \[ T^{-1}(0) \] The preimage of T is the set of polynomials where the following is true \[ T(ax+bx+cx^{2}+dx^{3})=0 \] This imp...
832 sym
Data 605-Homework3
Problem 1 (1) What is the rank of the matrix A? A <- matrix(c(1,2,3,4, -1,0,1,3, 0,1,-2,1, 5,4,-2,-3), 4, byrow=T) qr(A)$rank ## [1] 4 The rank is the same as the dimension. (2) Given an mxn matrix where m > n, what can be the maximum rank? The minimum rank, assuming that the matrix is non-zero? Giv...
567 sym R (856 sym/9 pcs)
Data 605-Discussion3
Problem C24 Using R A = matrix(c(1,-1,1,-1,1,-1,1,-1,1), nrow=3, ncol=3, byrow = T) A ## [,1] [,2] [,3] ## [1,] 1 -1 1 ## [2,] -1 1 -1 ## [3,] 1 -1 1 Av <- eigen(A) Av ## eigen() decomposition ## $values ## [1] 3.000000e+00 8.881784e-16 0.000000e+00 ## ## $vectors ## [,1] [,2] [,3] ## ...
234 sym R (441 sym/5 pcs)
Data 605-Discussion2
The determinant is a function that takes a square matrix as an input and produces a scalar as an output. So unlike a vector space, it is not an algebraic structure. However, it has many beneficial properties for studying vector spaces, matrices and systems of equations, so it is hard to ignore (though some have tried). While the properties of a d...
621 sym R (241 sym/6 pcs)
Data 605-Homework1
Problem Set 1 You can think of vectors representing many dimensions of related information. For instance, Netlfix might store all the ratings a user gives to movies in a vector. This is clearly a vector of very large dimensions (in the millions) and very sparse as the user might have rated only a few movies. Similarly, Amazon might store the item...
2211 sym R (1436 sym/21 pcs)
Data 605-Discussion1
Solving Systems of Linear Equations This exercise will consider the solving of linear equations simultaneously. The equations involve a more precise meaning that all the values of some variable quantities makes an equation, or several equations, simultaneously true. A system of linear equations is a collection of m equations in the variable quant...
2081 sym R (438 sym/9 pcs)
DATA 606 Data Project-Final
Loading Packages library(foreign) library(tidyr) library(dplyr) ## ## Attaching package: 'dplyr' ## The following objects are masked from 'package:stats': ## ## filter, lag ## The following objects are masked from 'package:base': ## ## intersect, setdiff, setequal, union library(psych) library(ggplot2) ## ## Attaching package...
5827 sym R (6656 sym/60 pcs) 10 img
Data 606-Lab9-Multiple Linear Regression
Grading the professor Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. However, the use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related charac...
10215 sym R (6926 sym/32 pcs) 8 img 2 tbl
Data 606-Homework9
Baby weights, Part I. (9.1, p. 350) The Child Health and Development Studies investigate a range of topics. One study considered all pregnancies between 1960 and 1967 among women in the Kaiser Foundation Health Plan in the San Francisco East Bay area. Here, we study the relationship between smoking and weight of the baby. The variable smoke is c...
8068 sym R (819 sym/11 pcs) 2 img