Publications by Farhana Zahir
FZahir_Assignment04
Problem Set 1 Verify using R that SVD and Eigenvalues are related A <- matrix(c(1,2,3, -1, 0, 4), nrow = 2, ncol = 3, byrow = TRUE) Compute the left-singular, singular values, and right-singular vectors of A using the svd command. The vector d contains the singular values The matrix u contains the left singular vectors (rows). The matrix v contai...
1081 sym R (3146 sym/33 pcs)
FZahirDiscussion4
Problem C25 page 443 Define the linear transformation \[T:\mathbb{C}^3 \rightarrow \mathbb{C}^2, T \bigg(\begin{vmatrix}x_1\\x_2\\x_3\end{vmatrix}\bigg)=\begin{vmatrix} 2x_1-x_2+5x_3 \\ -4x_1+2x_2-10x_3\end{vmatrix}\] Verify that T is a linear transformation Solution: If T is a linear transformation and a and b are vectors and c is a scaler, then...
1176 sym
Data608Assignment01
Principles of Data Visualization and Introduction to ggplot2 I have provided you with data about the 5,000 fastest growing companies in the US, as compiled by Inc. magazine. lets read this in: inc <- read.csv("https://raw.githubusercontent.com/charleyferrari/CUNY_DATA_608/master/module1/Data/inc5000_data.csv", header= TRUE) And lets preview this...
2935 sym R (6176 sym/16 pcs) 4 img
FZahirDiscussion3
Problem C10 page 388 Find the charactertistic polynomial of the matrix library(knitr) library(pracma) A = matrix(c (1,2,3,4), nrow=2, byrow=T) print(A) ## [,1] [,2] ## [1,] 1 2 ## [2,] 3 4 Solution using R charpoly(A) ## [1] 1 -5 -2 This gives us the characteristic polynomial as below: \[{ PA(x)=λ}^{ 2 }-5{ λ } -2\] Solu...
790 sym R (162 sym/5 pcs)
Data 605 Assignment 02
Problem Set 1 Show that ATA!=AAT in general. (Proof and demonstration) #Let us take a 4X3 matrix mat1 mat1<-matrix(1:12,nrow=4, byrow=T) mat1 ## [,1] [,2] [,3] ## [1,] 1 2 3 ## [2,] 4 5 6 ## [3,] 7 8 9 ## [4,] 10 11 12 #Calculate the transpose of mat1, this is a 3X4 matrix mat1_transpose<-t(mat1) ma...
831 sym R (4000 sym/39 pcs)
FZahirDiscussion2Response
Constructing the matrix and calculating determinant A <- matrix(c(1, 2, 1, 2, 0, 1, 2, 3, 7/4), nrow=3, byrow=T) A ## [,1] [,2] [,3] ## [1,] 1 2 1.00 ## [2,] 2 0 1.00 ## [3,] 2 3 1.75 print(det(A)) ## [1] 0 Trying to find inverse using solve print(solve(A)) ##Error: Lapack routine dgesv: system is exactly singular: U[3...
396 sym R (634 sym/10 pcs)
FZahirDiscussion2
Ex C25 Pg 353 Calculating determinant of a 3 X 3 matrix Doing the computations by hand, find the determinant of the matrix below: mat = matrix(c (3,-1,4,2,5,1,2,0,6), ncol=3 , nrow=3, byrow=TRUE) mat ## [,1] [,2] [,3] ## [1,] 3 -1 4 ## [2,] 2 5 1 ## [3,] 2 0 6 Steps to calculate the determinant of the 3 X 3 matr...
343 sym R (978 sym/12 pcs)
Data605HW01
Problem 01 (1) Calculate the dot product u:v where u = [0.5;0.5] and v= [3;-4] u <- c(0.5,0.5) v <- c(3,-4) ##Dot product without using R function dotprod<-u[1]*v[1]+u[2]*v[2] dotprod ## [1] -0.5 ##Dot product using R function library('pracma') dotprod1<-dot(u,v) dotprod1 ## [1] -0.5 (2) What are the lengths of u and v? ##Length u len_...
449 sym R (2745 sym/16 pcs)
Data605Discussion1response
Problem 3 page 41 Using R to build the matrix a<-matrix(c(2,3,-1,0,1,2,1,3,1,3,3,7), nrow=3, byrow=TRUE) a ## [,1] [,2] [,3] [,4] ## [1,] 2 3 -1 0 ## [2,] 1 2 1 3 ## [3,] 1 3 3 7 b<-matrix(c(0,3,7),nrow=3) b ## [,1] ## [1,] 0 ## [2,] 3 ## [3,] 7 Results: X1=1, X2=0, X3=2 Row echelon us...
147 sym R (717 sym/12 pcs)
Data605Discussion01
Matrix Multiplication Ex C26, page 191, A first Course in Linear Algebra, Beezer Question: Compute the product AB of the two matrices below using Matrix Multiplication(MM) Constructing the matrix A<-matrix(c(1,3,1,0,1,0,1,1,2),nrow=3,byrow=TRUE) A ## [,1] [,2] [,3] ## [1,] 1 3 1 ## [2,] 0 1 0 ## [3,] 1 1 2 B<...
635 sym R (1115 sym/10 pcs)