# Linear Algebra

All I want is a good introduction. and problem 2 and 3.
problem 2:
Result from coding:
Highest eigenvalue:3.6412
Corresponding eigenvector: 0.4747
0.1797
0.4067
0.5371
0.5371
Coding for problem 2 and 3:

clear all; close all, clc;
A= [1 1 0 1 1; 1 1 0 0 0; 0 0 1 1 1; 1 0 1 1 1; 1 0 1 1 1];
display(A);
[V,D]=eig(A);
display(V);
display(D);

What is an eigenvalue? How does it relate to its eigenvector? Interpret the largest
eigenvalue and its eigenvector pair in the problem above in the context of our movie
ratings in relation to genre.
(b) If the original matrix represents lms that you enjoyed, what would our eigenvector
imply about lms you would like to watch in the future? (Hint: Consider the direction
of the eigenvector – towards which movies is it pointing and why? In other words, what
are the rows corresponding to the most prominent members of your eigenvector? These
are the top&quot; movies highlighted by our algorithm.)
(c) Why, in our analysis, is Robin Hood classied as a lower title than, say, Shrek, even
though they have the same number of relationships to other lms in the matrix?All I want is a good introduction. and problem 2 and 3.
problem 2:
Result from coding:
Highest eigenvalue:3.6412
Corresponding eigenvector: 0.4747
0.1797
0.4067
0.5371
0.5371
Coding for problem 2 and 3:

clear all; close all, clc;
A= [1 1 0 1 1; 1 1 0 0 0; 0 0 1 1 1; 1 0 1 1 1; 1 0 1 1 1];
display(A);
[V,D]=eig(A);
display(V);
display(D);

What is an eigenvalue? How does it relate to its eigenvector? Interpret the largest
eigenvalue and its eigenvector pair in the problem above in the context of our movie
ratings in relation to genre.
(b) If the original matrix represents lms that you enjoyed, what would our eigenvector
imply about lms you would like to watch in the future? (Hint: Consider the direction
of the eigenvector – towards which movies is it pointing and why? In other words, what
are the rows corresponding to the most prominent members of your eigenvector? These
are the top&quot; movies highlighted by our algorithm.)
(c) Why, in our analysis, is Robin Hood classied as a lower title than, say, Shrek, even
though they have the same number of relationships to other lms in the matrix?

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