I have problems finding the eigenvectors of a 3 x 3 matrix. Can anyone help?

Name:

manw1992

Top Lectures

Lecture 1 - The Moral Side of Murder

Lecture 5 - Nash Equilibrium

Lecture 9 - 2-Node Truss Element-Total Lagrangian Formulation

Lecture 31 - Simplex method in linear programming

Lecture 3 - Electric Flux and Gauss's Law

Lecture 2 - Euler's Numerical Method for y'=f(x,y) and its Generalizations

Lecture 4 - Commutators and Time Evolution (the Time Dependent Schrodinger Equation)

Lecture 4 - American Puritanism I

Lecture 7 - The Loop and a Half Problem

Lecture 8 - Maxillary Premolars

Popular this Week

Law

Lecture 3 - The UN's role in Overcoming Development Challenges

Arts

Lecture 2 - Van Eyck, Portrait of Giovanni Arnolfini and his Wife, 1434

Sciences

Lecture 3 - Electric Flux and Gauss's Law

Social Sciences

Lecture 5 - Nash Equilibrium

Engineering

Lecture 1 - Laser Fundamentals I

Humanities

Lecture 1 - The Moral Side of Murder

Mathematics

Lecture 1 - Differential and Integral Calculus 1

Medicine

Lecture 14 - What if Saliva Were Red (with permission from the University of Pittsburgh)

Say matrix A is 3x3. Let g be the eigenvalue, i.e. a scalar parameter, associated with the matrix. Let v be the 3x1 non-zero eigenvector associated with this eigenvalue. Then A.v=g.v --> (A-g.I)v=0 --> I is the 3x3 unit matrix. g exists if (A-g.I) is non-invertible, which happens only if its determinant is 0 i.e. det(A-g.I)=0. So calculating the determinant of this (that is you subtract g as an unknown scalar from each diagonal entry of A and calculate the determinant of the result), and setting it equal to 0 gives you an equation in one unknown, g, which you can solve (the characteristic equation). It can give multiple solutions for g, all of which are eigenvalues of the matrix A. After you do that, you solve the matrix equation (A-g.I).v=0 for each eigenvalue g you found, which will yield one eigenvector v (with parameters v1,v2,v3 which you can find) defined as a vector times a scalar for each eigenvalue.

For more details and examples see Khan's lectures in Linear Algebra 132-137 and especially lecture 137 http://www.theopenacademy.com/content/lecture-137-linear-algebra-eigenve....

Hope that helped.

Thanks that makes sense now.

If you still don't have answer to this problem I suggest you to visit StudyGeek.org they can help you a lot.

“Determine never to be idle. No person will have occasion to complain of the want of time, who never loses any. It is wonderful how much may be done, if we are always doing.”

― Thomas Jefferson

This content is written very well. Your use of formatting when making your points makes your observations very clear and easy to understand. Thank you. Keep doing like this.

http://www.gistnetwork.org/node/47473

https://twitter.com/1HostingDeal

https://www.storeboard.com/webhostingonedollar

http://www.eioba.com/a/5j9q/one-dollar-web-hosting

http://www.lasplash.com/event/43035-web-hosting-one-dollar

https://webhostingonedollar.wordpress.com/

https://webhostingonedollars.tumblr.com/