ASSIGNMENT 2

IS 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS

1. Problem set 1

(1) Show that AT A 6= AAT

in general. (Proof and demonstration.)

(2) For a special type of square matrix A, we get AT A = AAT

. Under what conditions

could this be true? (Hint: The Identity matrix I is an example of such a matrix).

Please typeset your response using LaTeX mode in RStudio. If you do it in paper, please

either scan or take a picture of the work and submit it. Please ensure that your image is

legible and that your submissions are named using your first initial, last name, assignment

and problem set within the assignment. E.g. LFulton_Assignment2_PS1.png

2. Problem set 2

Matrix factorization is a very important problem. There are supercomputers built just

to do matrix factorizations. Every second you are on an airplane, matrices are being

factorized. Radars that track flights use a technique called Kalman filtering. At the heart

of Kalman Filtering is a Matrix Factorization operation. Kalman Filters are solving linear

systems of equations when they track your flight using radars.

Write an R function to factorize a square matrix A into LU or LDU, whichever you

prefer. Please submit your response in an R Markdown document using our class naming

convention, E.g. LFulton_Assignment2_PS2.png

You don’t have to worry about permuting rows of A and you can assume that A is less

than 5×5, if you need to hard-code any variables in your code. If you doing the entire

assignment in R, then please submit only one markdown document for both the problems.

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