Publications by Gregg Maloy
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The following webpages were referenced to preform this analysis, as was the professor’s blackboard example: https://rpubs.com/tahmad/DATA605Assignment4 https://rpubs.com/R-Minator/eigenshoes https://rpubs.com/jefflittlejohn/Data605_HW4 The following exercise uses Principle Component Analysis(PCA) to ‘build and visualize eigenimagery that acc...
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A First Course in Linear Algebra, Beezer, R., 2008 Page 403 Problem C10 Question In the vector space C3, compute the vector representation ρB (v) for the basis B and vector v below. \[ B = \left\{ \begin{pmatrix} 2 \\ -2 \\ 2 \end{pmatrix}, \begin{pmatrix} 1 \\ 3 \\ 1 \end{pmatrix}, \begin{pmatrix} 3 \\ 5 \\ 2 \end{pmatrix} \right\} \] \[ v...
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#install.packages("MASS") library(MASS) 1. What is the rank of matrix A. A =\(\begin{bmatrix}1 & 2 & 3 & 4 \\-1 & 0 & 1 & 3 \\ 0 & 1 &-2 & 1 \\ 5 & 4 &-2 &-3 \end{bmatrix}\) To solve we need row echelon form: Row operations Column 1: [2,1] must equal 0: Calculation: Row1+Row2 \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 2 & 4 & 7 \\ 0 & 1 &-2 ...
3285 sym R (834 sym/7 pcs)
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Find the characteristic polynomial of the matrix A. A =\(\begin{bmatrix}1 & 2 \\3 & 4\end{bmatrix}\) To solve we will use the equation det(A−λI)=0 A−λI =\(\begin{bmatrix}1-λ & 2 \\3 & 4-λ\end{bmatrix}\) Solve for λ: \[{det(A−λI)= (1-λ)(4-λ) - (2)(3) }\] \[{det(A−λI)=(λ^2-5λ+4)-6}\] \[{det(A−λI)=λ^2-5λ-2}\] Answer The ch...
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Problem 1 Show that ATA != AAT in general. (Proof and demonstration.) Here is an example to demonstrate that ATA != AAT. The below 3 x 3 matrix A will be used to demonstrate ATA != AAT. library(matrixcalc) A<- matrix(c(2,-3, 4, 1, 0,1,2,1,2), nrow = 3, byrow = TRUE) A ## [,1] [,2] [,3] ## [1,] 2 -3 4 ## [2,] 1 0 1 ## [...
2238 sym R (2656 sym/30 pcs)
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A First Course in Linear Algebra, Beezer, R., 2008 Question C23 page 278: Doing the computations by hand, find the determinant of the matrix below. 1 3 2 4 1 3 1 0 1 Define matrix Below a 3x3 matrix is coded and printed. A <- matrix(c(1, 4, 1, 3, 1,0 ,2 ,3 ,1 ), nrow = 3, byrow = FALSE) print(A) ## [,1] [,2] [,3] ## [1,] 1 3 2 ...
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A First Course in Linear Algebra, Beezer, R., 2008 C10, page 64 Compute matrix calculations Define matrix 1 matrix1 <- matrix(c(2, -3, 4, 1, 0), nrow = 5, byrow = TRUE) print(matrix1) ## [,1] ## [1,] 2 ## [2,] -3 ## [3,] 4 ## [4,] 1 ## [5,] 0 #Define matrix 2 matrix2 <- matrix(c(1, 2, -5, 2, 4), nrow = 5, byrow = TRUE) pr...
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Part 1: Assignment & Packages One of the most useful applications for linear algebra in data science is image manipulation. We often need to compress, expand, warp, skew, etc. images. To do so, we left multiply a transformation matrix by each of the point vectors. For this assignment: 1.) Build the first letters for both your first and last na...
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Assignment & Packages One of the most useful applications for linear algebra in data science is image manipulation. We often need to compress, expand, warp, skew, etc. images. To do so, we left multiply a transformation matrix by each of the point vectors. For this assignment: 1.) Build the first letters for both your first and last name using ...
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SMS Classification System Using TidyModels, Naive Bayes, Random Forest and XGBoost
Part 1: Assignment For this project, tidymodels was utilized to build a SMS classification system which flagged text messages as ‘spam’ or ‘ham’. Naive bayes, random forest and XGBoost models were then run to compare classification results across models. Part 2: Packages & Dataset The dataset used for this project is located at: https:/...
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