Homework 7
Debugging
Assigned: Friday, February 19
Due: Friday, February 26, 11:00AM (Hard Deadline)
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Applications of
Eigenvalues and
Eigenvectors
22.2
Introduction
Many applications of matrices in both engineering and science utilize eigenvalues and, sometimes, eigenvectors. Control theory, vibration analysis, electric circuits, advanced dynamics and
qua

LECTURE 15
Eigenvalues and Eigenvectors
1. Motivating Examples
Example 15.1. Consider the following linear transformation T : R3 R3 :
T ([x, y, z]) = [x, y cos() + z sin () , y sin() + z cos()]
The corresponding matrix is
1
0
0
AT = 0 cos() sin()
0 sin()

Chapter 16. Three-by-Three Eigenvalues and Eigenvectors
Take a 3 3 matrix
a11 a12 a13
A = a21 a22 a23 .
a31 a32 a33
As in the 2 2 case, we want to find numbers and nonzero vectors u in R3
satisfying
Au = u.
As before, the number is called an eigenvalue of

Generalized
Eigenvectors
Math 240
Definition
Computation
and Properties
Chains
Generalized Eigenvectors
Math 240 Calculus III
Summer 2013, Session II
Wednesday, July 31, 2013
Generalized
Eigenvectors
Agenda
Math 240
Definition
Computation
and Properties
C

Some Basic Matrix Theorems
Richard E. Quandt
Princeton University
Definition 1. Let A be a square matrix of order n and let be a scalar quantity. Then det(AI)
is called the characteristic polynomial of A.
It is clear that the characteristic polynomial is

Chapter 6
Eigenvalues and Eigenvectors
Po-Ning Chen, Professor
Department of Electrical and Computer Engineering
National Chiao Tung University
Hsin Chu, Taiwan 30010, R.O.C.
6.1 Introduction to eigenvalues
6-1
Motivations
The static system problem of Ax

A short example calculating eigenvalues and eigenvectors of a
matrix
We want to calculate the eigenvalues and the eigenvectors of matrix A:
2 1 0
A = 1 1 1
1 1 1
We start by using the Characteristic polynomial to find the eigenvectors:
2
1
0
det(I A) = de

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Homework 3
Shells, Environment, and Scripting
Due: Saturday, October 1, 10:00PM (Hard Deadline)
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Homework 6
Build Systems
Assigned: Friday, February 12, 11:00AM
Due: Friday, February 19, 11:00AM (Hard Deadline)
Submission Instructions
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Chapter 5
Eigenvalues and
Eigenvectors
In this chapter we return to the study of linear transformations that we started
in Chapter 3. The ideas presented here are related to finding the simplest
matrix representation for a fixed linear transformation. As